Simplicity of vacuum modules over affine Lie superalgebras

Details Simplicity of vacuum modules over affine Lie superalgebras Simplicity of vacuum modules over affine Lie superalgebras

2008-06-16

arxiv.org/abs/0806.2605v1

Mathematics

Representation Theory

16 pages

Scientific paper

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.

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