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arXiv · 0806.2605

Simplicity of vacuum modules over affine Lie superalgebras

Crystal Hoyt·Shifra Reif
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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.

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Crystal Hoyt, Shifra Reif. 2008-06-16. Simplicity of vacuum modules over affine Lie superalgebras. https://arxiv.org/abs/0806.2605

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