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A construction of some ideals in affine vertex algebrasMar 01 2001Mar 04 2001Let $N_{k} (\g)$ be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type $A_{\ell -1} ^{(1)}$ or $C_{\ell} ^{(1)}$. We construct a family of ideals $J_{m,n} (\g)$ in $N_{k} (\g)$, and a family $V_{m,n} ... More

A classification of irreducible Wakimoto modules for the affine Lie algebra $A_1 ^{(1)}$Feb 25 2014By using methods developed in arXiv:math/0602181 we study the irreducibility of certain Wakimoto modules for $\widehat{sl_2}$ at the critical level. We classify all $\chi \in {\Bbb C}((z))$ such that the corresponding Wakimoto module $W_{\chi}$ is irreducible. ... More

Lie superalgebras and irreducibility of A_1^(1)-modules at the critical levelFeb 09 2006We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the irreducibility ... More

A realization of certain modules for the $N=4$ superconformal algebra and the affine Lie algebra $A_2 ^{(1)}$Jul 06 2014We shall first present an explicit realization of the simple $N=4$ superconformal vertex algebra $L_{c} ^{N=4}$ with central charge $c=-9$. This vertex superalgebra is realized inside of the $ b c \beta \gamma $ system and contains a subalgebra isomorphic ... More

Fusion rules and complete reducibility of certain modules for affine Lie algebrasJul 31 2012Mar 26 2013We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary modules for affine ... More

On fusion rules and intertwining operators for the Weyl vertex algebraMar 25 2019In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra. This way we ... More

Some general results on conformal embeddings of affine vertex operator algebrasJan 24 2011May 30 2011We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer levels. In ... More

On Free Field Realizations of $W(2,2)$-ModulesMay 27 2016Jan 15 2017The aim of the paper is to study modules for the twisted Heisenberg-Virasoro algebra $\mathcal H$ at level zero as modules for the $W(2,2)$-algebra by using construction from [J. Pure Appl. Algebra 219 (2015), 4322-4342, arXiv:1405.1707]. We prove that ... More

Free field realization of the twisted Heisenberg-Virasoro algebra at level zero and its applicationsMay 07 2014Feb 15 2015We investigate the free fields realization of the twisted Heisenberg-Virasoro algebra $\mathcal{H}$ at level zero. We completely describe the structure of the associated Fock representations. Using vertex-algebraic methods and screening operators we construct ... More

Self-dual and logarithmic representations of the twisted Heisenberg--Virasoro algebra at level zeroMar 01 2017Mar 30 2018This paper is a continuation of arXiv:1405.1707. We present certain new applications and generalizations of the free field realization of the twisted Heisenberg-Virasoro algebra ${\mathcal H}$ at level zero. We find explicit formulas for singular vectors ... More

Lattice construction of logarithmic modules for certain vertex algebrasFeb 19 2009Sep 27 2009A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach, we give explicit vertex operator construction of certain indecomposable and logarithmic modules for the triplet vertex algebra ... More

Representations of certain non-rational vertex operator algebras of affine typeFeb 01 2007Oct 27 2007In this paper we study a series of vertex operator algebras of integer level associated to the affine Lie algebra $A_{\ell}^{(1)}$. These vertex operator algebras are constructed by using the explicit construction of certain singular vectors in the universal ... More

Whittaker modules for the affine Lie algebra $A_1 ^{(1)}$Sep 18 2014Nov 25 2015We prove the irreducibility of the universal non-degenerate Whittaker modules for the affine Lie algebra $\widehat{sl_2}$ of type $A_1^{(1)}$ with noncritical level which are also irreducible Whittaker modules over $\widetilde{sl_2} =\widehat{sl_2} + ... More

On principal realization of modules for the affine Lie algebra $A_1 ^{(1)}$ at the critical levelDec 10 2015We present complete realization of irreducible $A_1 ^{(1)}$-modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. ... More

Realizations of simple affine vertex algebras and their modules: the cases $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$Nov 30 2017Jan 31 2019We study embeddings of the simple admissible affine vertex algebras $V_k(sl(2))$ and $V_k(osp(1,2))$, $k \notin {\Bbb Z}_{\ge 0}$, into the tensor product of rational Virasoro and $N=1$ Neveu-Schwarz vertex algebra with lattice vertex algebras. We prove ... More

A note on the affine vertex algebra associated to $\frak{gl}(1 \vert 1)$ at the critical level and its generalizationsJun 28 2017In this note we present an explicit realization of the affine vertex algebra $V^{cri}(\frak{gl}(1 \vert 1)) $ inside of the tensor product $F\otimes M$ where $F$ is a fermionic verex algebra and $M$ is a commutative vertex algebra. This immediately gives ... More

Classification of irreducible modules of certain subalgebras of free boson vertex algebraJul 18 2002Let M(1) be the vertex algebra for a single free boson. We classify irreducible modules of certain vertex subalgebras of M(1) generated by two generators. These subalgebras correspond to the W(2, 2p-1)--algebras with central charge $1- 6 \frac{(p - 1) ... More

A construction of admissible $A_1^{(1)}$-modules of level $-{4/3}$Jan 05 2004Feb 03 2004By using generalized vertex algebras associated to rational lattices, we construct explicitly the admissible modules for the affine Lie algebra $A_1 ^{(1)}$ of level $-{4/3}$. As an application, we show that the W(2,5) algebra with central charge c=-7 ... More

On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebraNov 12 2018Jul 01 2019We extend the Dong-Mason theorem on the irreducibility of modules for orbifold vertex algebras from [C. Dong, G. Mason, Duke Math. J. 86 (1997)] 305-321] for the category of weak modules. Let $V$ be a vertex operator algebra, $g$ an automorphism of order ... More

On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebraNov 12 2018We extend the Dong-Mason theorem on the irreducibility of modules for orbifold vertex algebras from [C. Dong, G. Mason, Duke Math. J. 86 (1997)] 305-321] for the category of weak modules. Let $V$ be a vertex operator algebra, $g$ an automorphism of order ... More

Regularity of certain vertex operator algebras with two generatorsNov 06 2001For every $m \in {\C} \setminus \{0, -2\}$ and every nonnegative integer $k$ we define the vertex operator (super)algebra $D_{m,k}$ having two generators and rank $ \frac{3 m}{m + 2}$. If $m$ is a positive integer then $D_{m,k}$ can be realized as a subalgebra ... More

The structure of Zhu's algebras for certain W-algebrasJun 26 2010May 17 2011We introduce a new approach that allows us to determine the structure of Zhu's algebra for certain vertex operator (super)algebras which admit horizontal $\mathbb{Z} $-grading. By using this method and an earlier description of Zhu's algebra for the singlet ... More

Some applications and constructions of intertwining operators in LCFTMay 18 2016We discuss some applications of fusion rules and intertwining operators in the representation theory of cyclic orbifolds of the triplet vertex operator algebra. We prove that the classification of irreducible modules for the orbifold vertex algebra W(p)^{A_m} ... More

On free field realizations of $W(2,2)$--modulesMay 27 2016The aim of the paper is to study modules for the twisted Heisenberg--Virasoro algebra $\mathcal H$ at level zero as modules for the $W(2,2)$--algebra by using construction from arXiv:1405.1707v2. We prove that the irreducible highest weight ${\mathcal ... More

Kostant's pair of Lie type and conformal embeddingsFeb 08 2018We deal with some aspects of the theory of conformal embeddings of affine vertex algebras, providing a new proof of the Symmetric Space Theorem and a criterion for conformal embeddings of equal rank subalgebras. We finally study some examples of embeddings ... More

An application of collapsing levels to the representation theory of affine vertex algebrasJan 30 2018Oct 27 2018We discover a large class of simple affine vertex algebras $V_{k} (\mathfrak g)$, associated to basic Lie superalgebras $\mathfrak g$ at non-admissible collapsing levels $k$, having exactly one irreducible $\mathfrak g$-locally finite module in the category ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositionsApr 04 2016May 20 2016This paper is a continuation of arXiv:1602.04687. We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\mathfrak g, \theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\mathcal ... More

ADE subalgebras of the triplet vertex algebra W(p): A-seriesDec 21 2012May 21 2013Motivated by \cite{am1}, for every finite subgroup $\Gamma \subset PSL(2,\mathbb{C})$ we investigate the fixed point subalgebra $\triplet^{\Gamma}$ of the triplet vertex $\mathcal {W}(p)$, of central charge $1-\frac{6(p-1)^{2}}{p}$, $p\geq2$. This part ... More

ADE subalgebras of the triplet vertex algebra W(p): D_m-seriesApr 21 2013We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex algebra $\bar{M(1)} ... More

Vertex Algebras $\mathcal{W}(p)^{A_m}$ and $\mathcal{W}(p)^{D_m}$ and Constant Term IdentitiesMar 05 2015We consider $AD$-type orbifolds of the triplet vertex algebras $\mathcal{W}(p)$ extending the well-known $c=1$ orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras $A(\mathcal{W}(p)^{A_m})$ and $A(\mathcal{W}(p)^{D_m})$, where ... More

Visual definition of procedures for automatic virtual scene generationFeb 10 2012With more and more digital media, especially in the field of virtual reality where detailed and convincing scenes are much required, procedural scene generation is a big helping tool for artists. A problem is that defining scene descriptions through these ... More

On classification of non-equal rank affine conformal embeddings and applicationsFeb 20 2017Dec 16 2017We complete the classification of conformal embeddings of a maximally reductive subalgebra $\mathfrak k$ into a simple Lie algebra $\mathfrak g$ at non-integrable non-critical levels $k$ by dealing with the case when $\mathfrak k$ has rank less than that ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural resultsFeb 15 2016Apr 17 2016We find all values of $k\in \mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\mathfrak g,\theta)$ is conformal, where $\mathfrak g$ is a basic simple Lie superalgebra and $-\theta$ its minimal ... More

Finite vs infinite decompositions in conformal embeddingsSep 22 2015Apr 06 2016Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras $V_{\mathbf{k}}(\mathfrak g^0)\subset V_{k}(\mathfrak g)$, corresponding to an embedding of a maximal equal rank reductive subalgebra $\mathfrak ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositionsApr 04 2016Apr 12 2017We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\mathfrak g, \theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\mathcal V_k(\mathfrak g^{\natural})$. A particular ... More

U-J Synergy Effect for the High Tc SuperconductorsSep 07 2004Dec 22 2004Using renormalization group and exact diagonalization of small clusters we investigate the ground state phase diagram of a two-dimensional extended Hubbard model with nearest-neighbor exchange interaction J, in addition to the local Coulomb repulsion ... More

Backreaction of a massless minimally coupled scalar field from inflationary quantum fluctuationsAug 27 2013In this paper we study a massless, minimally coupled scalar field in a FLRW spacetime with periods of different constant deceleration parameter. We assume the Bunch-Davies vacuum during inflation and then use a sudden matching approximation to match it ... More

Competing SDW Phases and Quantum Oscillations in (TMTSF)2ClO4 in Magnetic FieldOct 21 2002We propose a new approach for studying spin density waves (SDW) in the Bechgaard salt (TMTSF)2ClO4 where lattice is dimerized in transverse direction due to anion ordering. The SDW response is calculated in the matrix formulation that rigorously treats ... More

Reviving Threshold-Moving: a Simple Plug-in Bagging Ensemble for Binary and Multiclass Imbalanced DataJun 28 2016Jun 20 2017Class imbalance presents a major hurdle in the application of data mining methods. A common practice to deal with it is to create ensembles of classifiers that learn from resampled balanced data. For example, bagged decision trees combined with random ... More

Reviving Threshold-Moving: a Simple Plug-in Bagging Ensemble for Binary and Multiclass Imbalanced DataJun 28 2016Jul 03 2016Class imbalance presents a major hurdle in the application of data mining methods. A common practice to deal with it is to create ensembles of classifiers that learn from resampled balanced data. For example, bagged decision trees combined with random ... More

Exact solution of the magnetic breakdown problem in quasi-one-dimensional geometryNov 19 2003We present exact solution of the problem of electronic wave functions of quasi one-dimensional band with an inter-band gap at the Fermi surface and in the presence of magnetic field. The details of the analyzed model are appropriate to the situation in ... More

Comparison of different algorithms for under-sampled image reconstructionMar 05 2019The Compressive Sensing (CS) as a novel acquisition approach that finds its usage in image processing. The hypothesis like this one assures signal recovery with high quality from decreased number of samples compared with the number required by the Nyquist ... More

Energy Efficient Service Delivery in Clouds in Compliance with the Kyoto ProtocolApr 30 2012Cloud computing is revolutionizing the ICT landscape by providing scalable and efficient computing resources on demand. The ICT industry - especially data centers, are responsible for considerable amounts of CO2 emissions and will very soon be faced with ... More

Intrinsic group behaviour: dependence of pedestrian dyad dynamics on principal social and personal featuresMar 08 2017Oct 05 2018Being determined by human social behaviour, pedestrian group dynamics depends on "intrinsic properties" of the group such as the purpose of the pedestrians, their personal relation, their gender, age, and body size. In this work we quantitatively study ... More

The maximum entropy production principle and linear irreversible processesMar 18 2010It is shown that Onsager's principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is argued, in the ... More

The Impact of a Deep-Water Plunging Breaker on a Partially Submerged CubeDec 17 2017The impact of a plunging breaker on a partially submerged cube is explored experimentally in a wave tank equipped with a programable wave maker. The experiments are conducted with the cube (dimension $L=30.48$ cm) positioned at one streamwise location ... More

The Impact of a Deep-Water Plunging BreakerOct 07 2014The impact of a plunging breaking wave (wavelength approximately 1.3m) on a rigidly mounted rigid cube structure (dimension 0.31m) that is partially submerged is explored through experiments and numerical calculations. The experiments are carried out ... More

A Comparison of Model-Scale Experimental Measurements and Computational Predictions for a Large Transom-Stern WaveOct 07 2014The flow field generated by a transom stern hull form is a complex, broad-banded, three-dimensional system marked by a large breaking wave. This unsteady multiphase turbulent flow feature is difficult to study experimentally and simulate numerically. ... More

Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I) - A class-M fundamental physics mission proposal for Cosmic Vision 2015-2025: 2010 UpdateApr 01 2011This paper on ASTROD I is based on our 2010 proposal submitted for the ESA call for class-M mission proposals, and is a sequel and an update to our previous paper [Experimental Astronomy 23 (2009) 491-527; designated as Paper I] which was based on our ... More