On the one-dimensional representations of finite W-superalgebras for \mathfrakgl_M|N

2024/09/24 by Yang, Fanlei, Zeng, Yang
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2409.16014

Abstract

Let \mathfrakg=\mathfrakgl_M|N(\mathbbk) be the general linear Lie superalgebra over an algebraically closed field \mathbbk of characteristic zero. Fix an arbitrary even nilpotent element e in \mathfrakg and let U(\mathfrakg,e) be the finite W-superalgebra associated to the pair (\mathfrakg,e). In this paper we will give a complete classification of one-dimensional representations for U(\mathfrakg,e). To achieve this, we use the tool of shifted super Yangians to determine the commutative quotients of the finite W-superalgebras.

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