total 2109took 0.10s

Complete reducibility and Steinberg endomorphismsDec 27 2010Let G be a connected reductive algebraic group defined over an algebraically closed field of positive characteristic. We study a generalization of the notion of G-complete reducibility in the context of Steinberg endomorphisms of G. Our main theorem extends ... More

On inductively free reflection arrangementsAug 15 2012Mar 01 2013Suppose that W is a finite, unitary reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each such reflection arrangement A is free. There is the stronger notion of an ... More

Inductively free Multiderivations of Braid arrangementsFeb 09 2015Jan 18 2016The reflection arrangement of a Coxeter group is a well known instance of a free hyperplane arrangement. In 2002, Terao showed that equipped with a constant multiplicity each such reflection arrangement gives rise to a free multiarrangement. In this note ... More

The topology of arrangements of ideal typeJan 22 2018Oct 24 2018In 1962, Fadell and Neuwirth showed that the configuration space of the braid arrangement is aspherical. Having generalized this to many real reflection groups, Brieskorn conjectured this for all finite Coxeter groups. This in turn follows from Deligne's ... More

Inductive Freeness of Ziegler's Canonical Multiderivations for Reflection ArrangementsMay 08 2017Jul 14 2018Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger freeness property of inductive ... More

Some remarks on free arrangementsMar 02 2019We exhibit a particular free subarrangement of a certain restriction of the Weyl arrangement of type $E_7$ and use it to give an affirmative answer to a recent conjecture by T.~Abe on the nature of additionally free and stair-free arrangements.

Parabolic conjugacy in general linear groupsNov 25 2006Mar 21 2007Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL(n,q). We show that the number of P(q)-conjugacy classes in GL(n,q) is, as a function of q, a polynomial in q with integer coefficients. ... More

Cohomology of Coxeter arrangements and Solomon's descent algebraJan 11 2011Mar 08 2013We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group $W$ and relate it to the descent algebra of $W$. As a result, we claim that both the group algebra of $W$, as well as the Orlik-Solomon ... More

On the $K(π, 1)$-problem for restrictions of complex reflection arrangementsAug 17 2017Jan 01 2019Let $W\subset GL(V)$ be a complex reflection group, and ${\mathscr A}(W)$ the set of the mirrors of the complex reflections in $W$. It is known that the complement $X({\mathscr A}(W))$ of the reflection arrangement ${\mathscr A}(W)$ is a $K(\pi,1)$ space. ... More

Divisionally free Restrictions of Reflection ArrangementsOct 01 2015Sep 01 2017We study some aspects of divisionally free arrangements which were recently introduced by Abe. Crucially, Terao's conjecture on the combinatorial nature of freeness holds within this class. We show that while it is compatible with products, surprisingly, ... More

Arrangements of ideal typeJun 02 2016Jun 08 2016In 2006 Sommers and Tymoczko defined so called arrangements of ideal type A_I stemming from ideals I in the set of positive roots of a reduced root system. They showed in a case by case argument that A_I is free if the root system is of classical type ... More

Cocharacter-closure and spherical buildingsJun 01 2015Sep 28 2015Let $k$ be a field, let $G$ be a reductive $k$-group and $V$ an affine $k$-variety on which $G$ acts. In this note we continue our study of the notion of cocharacter-closed $G(k)$-orbits in $V$. In earlier work we used a rationality condition on the point ... More

Divisionally free Restrictions of Reflection ArrangementsOct 01 2015We study some aspects of divisionally free arrangements which were recently introduced by Abe. Crucially, Terao's conjecture on the combinatorial nature of freeness holds within this class. We show that while it is compatible with products, surprisingly, ... More

Arrangements of ideal typeJun 02 2016Apr 17 2017In 2006 Sommers and Tymoczko defined so called arrangements of ideal type A_I stemming from ideals I in the set of positive roots of a reduced root system. They showed in a case by case argument that A_I is free if the root system is of classical type ... More

Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and fourOct 01 2011Jun 16 2012In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group $W$ afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced from linear characters of centralizers ... More

On supersolvable reflection arrangementsSep 10 2012May 02 2013Let A = (A,V) be a complex hyperplane arrangement and let L(A) denote its intersection lattice. The arrangement A is called supersolvable, provided its lattice L(A) is supersolvable, a notion due to Stanley. Jambu and Terao showed that every supersolvable ... More

Reflection arrangements are hereditarily freeMay 24 2012Nov 05 2012Suppose that W is a finite, unitary, reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each such reflection arrangement A is free. Let L(A) be the intersection lattice ... More

On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebrasSep 06 2012Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\mathbbm k$ of characteristic zero. We consider the commuting variety $\mathcal C(\mathfrak u)$ of the nilradical $\mathfrak u$ of the Lie algebra $\mathfrak ... More

Spherical Nilpotent Orbits in Positive CharacteristicAug 07 2007May 27 2008Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we classify all the spherical nilpotent G-orbits in the Lie algebra of G. The classification ... More

Spherical subgroups in simple algebraic groupsMay 14 2013Aug 20 2014Let $G$ be a simple algebraic group. A closed subgroup $H$ of $G$ is called spherical provided it has a dense orbit on the flag variety $G/B$ of $G$. Reductive spherical subgroups of simple Lie groups were classified by Kr\"amer in 1979. In 1997, Brundan ... More

Alperin's Conjecture for Algebraic GroupsMar 14 2007Jul 06 2007We prove analogues for reductive algebraic groups of some results for finite groups due to Knoerr and Robinson which play a central role in their reformulation of Alperin's conjecture for finite groups.

The $K(π, 1)$-problem for restrictions of complex reflection arrangementsAug 17 2017In 1962, Fadell and Neuwirth showed that the configuration space of the braid arrangement is aspherical. Having generalized this to many real reflection groups, Brieskorn conjectured this for all Coxeter groups. This follows from Deligne's seminal work ... More

Support Varieties, AR-Components, and Good FiltrationsMar 13 2007Sep 21 2009In continuation of work begun in \cite{FR}, we study in this article those Auslander--Reiten components of the algebras $\Dist(G_r)$ that contain simple modules or baby Verma modules, where $\Dist(G_r)$ is the algebra of distributions of the $r$-th Frobenius ... More

Nice reflection arrangementsMay 18 2015The aim of this note is a classification of all nice and all inductively factored reflection arrangements. It turns out that apart from the supersolvable instances only the monomial groups $G(r,r,3)$ for $r \ge 3$ give rise to nice reflection arrangements. ... More

Ziegler's Multi-Reflection Arrangements are freeMar 19 2014Jun 27 2014In 1989, Ziegler introduced the concept of a multi-arrangement. One natural example is the reflection arrangement of a unitary reflection group with multiplicity given by the number of reflections associated with each hyperplane. For all but three irreducible ... More

Nice Restrictions of Reflection ArrangementsSep 22 2016In a recent paper, Hoge and the second author classified all nice and all inductively factored reflection arrangements. In this note we extend this classification by determining all nice and all inductively factored restrictions of reflection arrangements. ... More

Addition-Deletion Theorems for Factorizations of Orlik-Solomon Algebras and nice ArrangementsFeb 13 2014Jan 15 2016We study the notion of a nice partition or factorization of a hyperplane arrangement due to Terao from the early 1990s. The principal aim of this note is an analogue of Terao's celebrated addition-deletion theorem for free arrangements for the class of ... More

Localizations of inductively factored arrangementsFeb 20 2016We show that the class of inductively factored arrangements is closed under taking localizations. We illustrate the usefulness of this with an application.

Special involutions and bulky parabolic subgroups in finite Coxeter groupsJun 01 2004The conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short intrinsic characterisation ... More

Counting chambers in restricted Coxeter arrangementsJun 29 2017Solomon showed that the Poincar\'e polynomial of a Coxeter group $W$ satisfies a product decomposition depending on the exponents of $W$. This polynomial coincides with the rank-generating function of the poset of regions of the underlying Coxeter arrangement. ... More

On cocharacters associated to nilpotent elements of reductive groupsAug 08 2006Aug 08 2007Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we consider particular classes of connected reductive subgroups H of G and show that the cocharacters ... More

The Steinberg Variety and Representations of Reductive GroupsFeb 06 2008Oct 25 2008We give an overview of some of the main results in geometric representation theory that have been proved by means of the Steinberg variety. Steinberg's insight was to use such a variety of triples in order to prove a conjectured formula by Grothendieck. ... More

Calculating conjugacy classes in Sylow $p$-subgroups of finite Chevalley groupsJan 02 2008Sep 23 2008In earlier work, the first author outlined an algorithm for calculating a parametrization of the conjugacy classes in a Sylow $p$-subgroup $U(q)$ of a finite Chevalley group $G(q)$, valid when $q$ is a power of a good prime for $G(q)$. In this paper we ... More

Invariants of reflection groups, arrangements, and normality of decomposition classes in Lie algebrasJul 08 2010Feb 29 2012Suppose that W is a finite, unitary, reflection group acting on the complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in W, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism ... More

The homology of the Steinberg variety and Weyl group coinvariantsApr 13 2007Jul 31 2009Let G be a complex, connected, reductive algebraic group with Weyl group W and Steinberg variety Z. We show that the graded Borel-Moore homology of Z is isomorphic to the smash product of the coinvariant algebra of W and the group algebra of W.

Equivariant K-theory of generalized Steinberg varietiesFeb 19 2013Nov 25 2013We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra and double ... More

Counting conjugacy classes in the unipotent radical of parabolic subgroups of $\GL_n(q)$Jan 06 2009Jun 16 2009Let $q$ be a power of a prime $p$. Let $P$ be a parabolic subgroup of the general linear group $\GL_n(q)$ that is the stabilizer of a flag in $\FF_q^n$ of length at most 5, and let $U = O_p(P)$. In this note we prove that, as a function of $q$, the number ... More

On conjugacy of unipotent elements in finite groups of Lie typeNov 19 2007Jul 11 2008Let $\bfG$ be a connected reductive algebraic group defined over $\F_q$, where $q$ is a power of a prime $p$ that is good for $\bfG$. Let $F$ be the Frobenius morphism associated with the $\FF_q$-structure on $\bfG$ and set $G = \bfG^F$, the fixed point ... More

On 1-dimensional representations of finite W-algebras associated to simple Lie algebras of exceptional typeMay 22 2009Mar 19 2010We consider the finite $W$-algebra $U(\g,e)$ associated to a nilpotent element $e \in \g$ in a simple complex Lie algebra $\g$ of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a conjecture of Premet, ... More

Inductive and Recursive Freeness of Localizations of MultiarrangementsJan 26 2015Sep 21 2015The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free multiarrangements are compatible ... More

Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and sevenFeb 27 2013Let G(q) be a finite Chevalley group, where q is a power of a good prime p, and let U(q) be a Sylow p-subgroup of G(q). Then a generalized version of a conjecture of Higman asserts that the number k(U(q)) of conjugacy classes in U(q) is given by a polynomial ... More

On the Invariants of the Cohomology of Complements of Coxeter ArrangementsOct 05 2018May 13 2019We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group $W$. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of $W$-invariants ... More

On the Invariants of the Cohomology of Complements of Coxeter ArrangementsOct 05 2018We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group $W$. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of $W$-invariants ... More

Arrangements of ideal type are inductively freeNov 23 2017Jan 31 2019Extending earlier work by Sommers and Tymoczko, in 2016 Abe, Barakat, Cuntz, Hoge, and Terao established that each arrangement of ideal type $\mathcal{A}_\mathcal{I}$ stemming from an ideal $\mathcal{I}$ in the set of positive roots of a reduced root ... More

On the irreducibility of symmetrizations of cross-characteristic representations of finite classical groupsJan 10 2012Nov 05 2012Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be a quasisimple group of Lie type of characteristic $p\ne {\rm char}(k)$ acting irreducibly on $W$. Suppose also that $G$ is a classical group with natural module $W$, chosen minimally ... More

Restrictions of aspherical arrangementsMar 09 2018Sep 20 2018In this note we present examples of $K(\pi,1)$-arrangements which admit a restriction which fails to be $K(\pi,1)$. This shows that asphericity is not hereditary among hyperplane arrangements.

The modality of a Borel subgroup in a simple algebraic group of type $E_8$Feb 09 2018Let $G$ be a simple algebraic group over an algebraically closed field $k$, where $\mathrm{char}\, k$ is either 0 or a good prime for $G$. We consider the modality $\mathrm{mod}(B : \mathfrak u)$ of the action of a Borel subgroup $B$ of $G$ on the Lie ... More

Rational points on generalized flag varieties and unipotent conjugacy in finite groups of Lie typeFeb 01 2006Feb 29 2008Let $G$ be a connected reductive algebraic group defined over the finite field $\FF_q$, where $q$ is a power of a good prime for $G$. We write $F$ for the Frobenius morphism of $G$ corresponding to the $\FF_q$-structure, so that $G^F$ is a finite group ... More

The strong Centre Conjecture: an invariant theory approachMay 18 2010Dec 16 2011The aim of this paper is to describe an approach to a a strengthened form of J. Tits' Centre Conjecture for spherical buildings. This is accomplished by generalizing a fundamental result of G. R. Kempf from Geometric Invariant Theory and interpreting ... More

Complete reducibility and separable field extensionsFeb 23 2010Apr 14 2010Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies on the recently ... More

Relative $GL(V)$-complete reducibilityJun 08 2018Let $K$ be a reductive subgroup of a reductive group $G$ over an algebraically closed field $k$. Using the notion of relative complete reducibility, in previous work of Bate-Martin-Roehrle-Tange a purely algebraic characterization of the closed $K$-orbits ... More

An Inductive Approach to Coxeter Arrangements and Solomon's Descent AlgebraApr 04 2011Jun 12 2011In a recent paper we claimed that both the group algebra of a finite Coxeter group $W$ as well as the Orlik-Solomon algebra of $W$ can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of ... More

On reflection subgroups of finite Coxeter groupsJan 31 2011Jan 24 2012Let $W$ be a finite Coxeter group. We classify the reflection subgroups of $W$ up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup $R$ of $W$ the conjugacy class of its Coxeter elements to be ... More

On inductively free Restrictions of Reflection ArrangementsOct 07 2013Jul 21 2014Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last two authros, we classified all inductively free reflection arrangements ... More

On the coadjoint orbits of maximal unipotent subgroups of reductive groupsSep 16 2014Jan 26 2015Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \u its Lie algebra. We prove the separability of orbit maps and the connectedness of ... More

The orbit structure of Dynkin curvesAug 23 2006Jan 17 2007Let G be a simple algebraic group over an algebraically closed field k; assume that Char k is zero or good for G. Let \cB be the variety of Borel subgroups of G and let e in Lie G be nilpotent. There is a natural action of the centralizer C_G(e) of e ... More

Relative complete reducibility and normalised subgroupsOct 29 2018Nov 12 2018We study a relative variant of Serre's notion of $G$-complete reducibility for a reductive algebraic group $G$. We let $K$ be a reductive subgroup of $G$, and consider subgroups of $G$ which normalise the identity component $K^{\circ}$. We show that such ... More

Restricting invariants of unitary reflection groupsMar 01 2015Apr 25 2015Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction ... More

Restricting invariants of unitary reflection groupsMar 01 2015Nov 19 2016Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction ... More

On unipotent radicals of pseudo-reductive groupsApr 14 2017Sep 07 2018We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, our main theorem gives bounds on the nilpotency class of geometric unipotent radicals of standard pseudo-reductive groups, which ... More

Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and sixJan 23 2012Mar 08 2013In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group $W$ acting on the $p$th graded component of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers ... More

Complete Reducibility and SeparabilitySep 24 2007Aug 12 2008Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between ... More

G-complete reducibility in non-connected groupsMar 05 2013In this paper we present an algorithm for determining whether a subgroup H of a non-connected reductive group G is G-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, ... More

Freeness of multi-reflection arrangements via primitive vector fieldsMar 27 2017Apr 17 2019In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to multi-arrangements stemming from well-generated ... More

Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eightMar 25 2014Nov 15 2014In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the pth graded component of its Orlik-Solomon ... More

Freeness of multi-reflection arrangements via primitive vector fieldsMar 27 2017Mar 26 2018In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to multi-arrangements stemming from well-generated ... More

Cocharacter-closure and the rational Hilbert-Mumford TheoremNov 28 2014Oct 03 2016For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate ... More

On Tits' Centre Conjecture for Fixed Point SubcomplexesNov 26 2008Feb 16 2009We give a short and uniform proof of a special case of Tits' Centre Conjecture using a theorem of J-P. Serre and a result from our earlier work. We consider fixed point subcomplexes $X^H$ of the building $X = X(G)$ of a connected reductive algebraic group ... More

D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance ModelsSep 05 2009An exact correspondence is pointed out between conformal field theories in D dimensions and dual resonance models in D' dimensions, where D' may differ from D. Dual resonance models, pioneered by Veneziano, were forerunners of string theory. The analog ... More

Renormalization of $ΔB=2$ Transitions in the Static Limit Beyond Leading LogarithmsAug 05 1996The renormalization group evolution of $\Delta B=2$ transition operators is studied at leading order in heavy quark effective theory and at next-to-leading order in QCD. We calculate new contributions that were not taken into account in previous work ... More

Theoretical Update on Rare K DecaysFeb 18 2000We review the status of rare kaon decays, concentrating on modes with sensitivity to short-distance flavour physics.

CP Violation in K Decays and Rare DecaysDec 10 1996The present status of CP violation in decays of neutral kaons is reviewed. In addition selected rare decays of both K and B mesons are discussed. The emphasis is in particular on observables that can be reliably calculated and thus offer the possibility ... More

Pion-pion and pion-nucleon interactions in chiral perturbation theoryOct 31 1997Elastic pion-pion and pion-nucleon scattering are reviewed in the context of chiral perturbation theory. Theoretical results from systematic low-energy expansions to O(p^6) for pion-pion and to O(p^3) for pion-nucleon scattering are compared with experimental ... More

Low-energy QCDNov 24 1995After a brief introduction to chiral perturbation theory, the effective field theory of the standard model at low energies, two recent applications are reviewed: elastic pion-pion scattering to two-loop accuracy and the complete renormalized pion-nucleon ... More

Quantum ChromodynamicsApr 19 2006After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to perturbative QCD, ... More

"The numerical accuracy of truncated Ewald sums for periodic systems with long-range Coulomb interactions"Feb 10 1995Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in the Ewald formulation. ... More

Improved Reconstruction of Dipole Directions from Spherical Magnetic Field MeasurementsAug 03 2016Reconstructing magnetizations from measurements of the generated magnetic potential is highly non-unique. The matter of uniqueness can be improved, but not entirely resolved, by the assumption that the magnetization is locally supported. Here, we focus ... More

Spherical Potential Theory: Tools and ApplicationsJul 04 2016This paper provides an overview on tools from potential theory on the sphere and some applications in geoscience.

Mass distribution in our GalaxyMar 07 2002This article summarizes recent work on the luminosity and mass distribution of the Galactic bulge and disk, and on the mass of the Milky Way's dark halo. A new luminosity model consistent with the COBE NIR data and the apparent magnitude distributions ... More

Dynamical Masses of Elliptical GalaxiesMar 07 2002Recent progress in the dynamical analysis of elliptical galaxy kinematics is reviewed. Results reported briefly include (i) the surprisingly uniform anisotropy structure of luminous ellipticals, (ii) their nearly flat (to $\sim 2R_e$) circular velocity ... More

The Galactic Center He I Stars: Remains of a Dissolved Young Cluster?May 05 2000Oct 25 2000A massive young star cluster, initially embedded in its parent molecular cloud, will spiral into the Galactic Center from $\lta 30m_6^{1/2}\pc$ during the life-time of its most massive stars, if the combined total mass is $\sim 10^6m_6\msun$. On its way ... More

Mass Distribution and Bulge Formation in the Milky Way GalaxyAug 16 2006In its first part, this paper summarizes recent work on the mass and shape of the Galactic dark halo. The second part presents a review of the large-scale structure of the Milky Way, and of the evidence that the inner Galaxy is dominated by baryonic matter. ... More

Modelling Kinematics and Dark Matter: The Halos of Elliptical GalaxiesFeb 02 2005This review is focussed on the outer halos of elliptical galaxies. Its emphasis is on (i) planetary nebulae as test particles to trace the stellar kinematics at large radii, (ii) the observed angular momentum in elliptical galaxy halos and its theoretical ... More

Structure and Mass Distribution of the Milky Way Bulge and DiskOct 26 2000Nov 01 2000This article summarizes the structural parameters of the Galactic bulge and disk, and discusses the interpretation of the bulge microlensing observations and the determination of the Milky Way's luminous mass from the terminal velocity curve and the Oort ... More

Dynamics of the Bar at the Galactic CentreApr 12 1996The now substantial evidence for a rotating bar in the inner Galaxy and its dynamical implications are reviewed.

What is an Ordinal Latent Trait Model?Feb 17 2019Although various polytomous item response models are considered to be ordinal models there seems no general definition of an ordinal model available. Alternative concepts of ordinal models are discussed and it is shown that they coincide for classical ... More

The convenient setting for ultradifferentiable mappings of Beurling- and Roumiue-type defined by a weight matrixDec 18 2014Sep 22 2015We prove in a uniform way that all ultradifferentiable function classes of Roumieu- and of Beurling-type defined in terms of a weight matrix admit a convenient setting if the matrix satisfies some mild regularity conditions. We prove that these categories ... More

Stability index for chaotically driven concave mapsSep 11 2012We study skew product systems driven by a hyperbolic base map S (e.g. a baker map or an Anosov surface diffeomorphism) and with simple concave fibre maps on an interval [0,a] like h(x)=g(\theta) tanh(x) where g(\theta) is a factor driven by the base map. ... More

Post-Newtonian methods: Analytic results on the binary problemOct 15 2009A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field equations, the ... More

Radiative Corrections to Radiative B Decays: Exclusive B -> V gamma at NLONov 25 2002We discuss a model-independent framework for the analysis of the radiative B-meson decays B -> K* gamma and B -> rho gamma based on the heavy-quark limit of QCD. We present a factorization formula for the treatment of B -> V gamma matrix elements involving ... More

Heavy Quark TheoryFeb 09 2002These lectures describe the most important theoretical methods in b-physics. We discuss the formalism of effective weak Hamiltonians, heavy quark effective theory, the heavy quark expansion for inclusive decays of b-hadrons and, finally, the more recent ... More

Rare Kaon Decays - OverviewOct 24 2001The theory of rare $K$ decays is reviewed, emphasizing short-distance processes and the prospects to probe the physics of flavour. A brief overview of the subject is presented, along with a more detailed discussion of the theory of $K\to\pi\nu\bar\nu$ ... More

Nonlinear Stability of Newtonian Galaxies and Stars from a Mathematical PerspectiveJan 25 2005The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems which have in recent years been obtained by Yan Guo and the author in the context of the Vlasov-Poisson ... More

Nonlinear stability of homogeneous models in Newtonian cosmologyMar 21 1996We consider the Vlasov-Poisson system in a cosmological setting and prove nonlinear stability of homogeneous solutions against small, spatially periodic perturbations in the sup-norm of the spatial mass density. This result is connected with the question ... More

Interaction of massive stars with their surroundingsOct 18 2008Due to their short lifetimes but their enormous energy release in all stages of their lives massive stars are the major engines for the comic matter circuit. They affect not only their close environment but are also responsible to drive mass flows on ... More

Chiral symmetryMay 29 1998Broken chiral symmetry has become the basis for a unified treatment of hadronic interactions at low energies. After reviewing mechanisms for spontaneous chiral symmetry breaking, I outline the construction of the low--energy effective field theory of ... More

Analysis of Alternative Metrics for the PAPR Problem in OFDM TransmissionMay 09 2011The effective PAPR of the transmit signal is the standard metric to capture the effect of nonlinear distortion in OFDM transmission. A common rule of thumb is the log$(N)$ barrier where $N$ is the number of subcarriers which has been theoretically analyzed ... More

Consciousness Viewed in the Framework of Brain Phase Space Dynamics, Criticality, and the Renormalization GroupMar 07 2011To set the stage for viewing Consciousness in terms of brain phase space dynamics and criticality, I will first review currently prominent theoretical conceptualizations and, where appropriate, identify ill-advised and flawed notions in Theoretical Neuroscience ... More

Letting the Brain Speak for itselfJul 20 2011Metaphors of Computation and Information tended to detract attention from the intrinsic modes of neural system functions, uncontaminated by the observer's role for collection and interpretation of experimental data. Recognizing the self-referential mode ... More

Fractals in the Nervous System: conceptual Implications for Theoretical NeuroscienceOct 14 2009Apr 07 2010This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet ... More