Crystal Hoyt, Shifra Reif
Published 2008-06-16Version 1
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.
A family of representations of the affine Lie superalgebra $\widehat{\mathfrak{gl}_{m|n}}(\mathbb{C})$
Invariants of the vacuum module associated with the Lie superalgebra gl(1|1)
Weyl denominator identity for the affine Lie superalgebra gl(2|2)^
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