Simplicity of vacuum modules over affine Lie superalgebras

Crystal Hoyt; Shifra Reif

doi:10.1016/j.jalgebra.2009.02.003

Simplicity of vacuum modules over affine Lie superalgebras

Crystal Hoyt, Shifra Reif

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove an explicit condition on the level k for the irreducibility of a vacuum module V^k over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik and V.G. Kac. An immediate consequence of this work is the simplicity conditions for the corresponding minimal W-algebras obtained via quantum reduction, in all cases except when the level k is a non-negative integer.

Original language	English
Pages (from-to)	2861-2874
Number of pages	14
Journal	Journal of Algebra
Volume	321
Issue number	10
DOIs	https://doi.org/10.1016/j.jalgebra.2009.02.003
State	Published - 15 May 2009
Externally published	Yes

Keywords

Affine Lie superalgebra
Vacuum module
W-algebra

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10.1016/j.jalgebra.2009.02.003

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AB - We prove an explicit condition on the level k for the irreducibility of a vacuum module Vk over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik and V.G. Kac. An immediate consequence of this work is the simplicity conditions for the corresponding minimal W-algebras obtained via quantum reduction, in all cases except when the level k is a non-negative integer.

KW - Affine Lie superalgebra

KW - Vacuum module

KW - W-algebra

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Simplicity of vacuum modules over affine Lie superalgebras

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Keywords

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