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Quantum Langlands duality of representations of ${\mathcal{W}}$-algebras

Part of: Lie algebras and Lie superalgebras Groups and algebras in quantum theory

Published online by Cambridge University Press:  04 October 2019

Tomoyuki Arakawa  and
Edward Frenkel
Tomoyuki Arakawa
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan email arakawa@kurims.kyoto-u.ac.jp
Edward Frenkel
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA email frenkel@math.berkeley.edu
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Abstract

We prove duality isomorphisms of certain representations of ${\mathcal{W}}$-algebras which play an essential role in the quantum geometric Langlands program and some related results.

Keywords

Kac–Moody algebra𝓩-algebraDrinfeld–Sokolov reductionLanglands programduality

MSC classification

Primary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B68: Virasoro and related algebras 17B69: Vertex operators; vertex operator algebras and related structures 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 12 , December 2019 , pp. 2235 - 2262
Copyright
© The Authors 2019 

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