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 language | English |
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Pages (from-to) | 273-339 |
Journal | Advances in Mathematics |
Volume | 347 |
Early online date | 26 Feb 2019 |
DOIs | |
Publication status | Published - 30 Apr 2019 |
Keywords
- Lie superalgebras
- W-algebras