Quantum reduction for affine superalgebras
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In this article, the homological method of quantization of generalized Drinfeld-Sokolov reductions to affine superalgebras is extended, leading to a unified representation theory of super-conformal algesbras.Abstract:
We extend the homological method of quantization of generalized Drinfeld–Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.read more
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Finite vs affine W-algebras
Alberto De Sole,Victor G. Kac +1 more
TL;DR: In this article, the H-twisted Zhu algebra is defined in terms of an indefinite integral of the λ-bracket of the vertex algebra V. The main novelty of this definition is that it can be expressed as an associative algebra with a given Hamiltonian operator H.
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Quantum reduction and representation theory of superconformal algebras
Victor G. Kac,Minoru Wakimoto +1 more
TL;DR: In this paper, the structure and representations of a family of vertex algebras obtained from affine superalgeses by quantum reduction were studied. And the free field realizations and determinant formulas for all superconformal algesbras were obtained in a unified way.
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Shifted Yangians and finite W-algebras
TL;DR: In this paper, the authors give a presentation for the finite W-algebra associated to a nilpotent matrix in the general linear Lie algebra over C. In particular, the presentation is that of the Yangian of level l associated to gln, as was first observed by Ragoucy and Sorba.
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Modular data and verlinde formulae for fractional level wzw models i
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TL;DR: The modular properties of fractional level sl ˆ (2 ) -theories and the application of the Verlinde formula have a long and checkered history in conformal field theory as discussed by the authors.
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Representation theory of mathcal{W} -algebras
TL;DR: In this paper, the authors studied the representation theory of affine Lie algebras and showed that the character of each irreducible highest weight representation of a simple Lie algebra is completely determined by that of the corresponding highest weight representations of a corresponding Lie algebra.
References
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Journal ArticleDOI
Quantization of the Drinfeld-Sokolov reduction
Boris Feigin,Edward Frenkel +1 more
TL;DR: In this paper, the quantum Drinfeld-Sokolov reduction of the affine Kac-Moody algebra sl( n ) Λ gives the W n -algebra of Fateev-Zamolodchikov-Lukyanov.
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Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
Victor G. Kac,Minoru Wakimoto +1 more
TL;DR: It is shown that the modular invariant representations of the Virasoro algebra Vir are precisely the "minimal series" of Belavin et al.
Journal ArticleDOI
Infinite-dimensional algebras, Dedekind's η-function, classical möbius function and the very strange formula
Book ChapterDOI
Integrable Highest Weight Modules over Affine Superalgebras and Number Theory
Victor G. Kac,Minoru Wakimoto +1 more
TL;DR: The problem of representing an integer as a sum of squares of integers has had a long history as discussed by the authors, and Girard and Fermat gave an irrefutable proof of this conjecture in 1641.
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Characters and fusion rules for W-algebras via quantized Drinfeld-Sokolov reduction
TL;DR: In this article, the authors calculate characters and fusion coefficients for affine algebras obtained from modular invariant representations by the quantized Drinfeld-Sokolov reduction, using the cohomological approach.
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