Whittaker coinvariants for GL(m|n)

Jonathan Brundan, Simon Goodwin

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4 Citations (Scopus)
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Abstract

Let Wm|n be the (finite) W-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra glm|n(C). In this paper we study the Whittaker coinvariants functor, which is an exact functor from category O for glm|n(C) to a certain category of finite-dimensional modules over Wm|n. We show that this functor has properties similar to Soergel's functor V in the setting of category O for a semisimple Lie algebra. We also use it to compute the center of Wm|n explicitly, and deduce some consequences for the classification of blocks of O up to Morita/derived equivalence.
Original languageEnglish
Pages (from-to)273-339
JournalAdvances in Mathematics
Volume347
Early online date26 Feb 2019
DOIs
Publication statusPublished - 30 Apr 2019

Keywords

  • Lie superalgebras
  • W-algebras

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