Whittaker coinvariants for GL(m|n)
Whittaker coinvariants for GL(m|n)
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DOI：
10.1016/j.aim.2019.02.025
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发表时间：
2019-04
影响因子：
1.7
通讯作者：
Jonathan Brundan;Simon M. Goodwin
中科院分区：
文献类型：
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作者：
Jonathan Brundan;Simon M. Goodwin
设W m| n是一般线性李超代数gl m中主幂零轨道上的（有限）W-代数|n（C）。本文研究了惠特克共不变函子，它是一个正合函子|n（C）到某类W m上的有限维模|n.我们证明了这个函子具有类似于Soergel函子V在半单李代数范畴O的设置下的性质。我们也用它来计算W m的中心|n显式，并推导出后果的分类块O到森田/派生等价。
Let W m| n be the (finite) W-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra gl m| n (C). In this paper we study the Whittaker coinvariants functor, which is an exact functor from category O for gl m| n (C) to a certain category of finite-dimensional modules over W m| 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 W m| n explicitly, and deduce consequences for the classification of blocks of O up to Morita/derived equivalence.