Whittaker coinvariants for $\mathrm{GL}(m|n)$
| Autor: | Brundan, Jonathan, Goodwin, Simon M. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Adv. Math. 347 (2019), 273-339 |
| Druh dokumentu: | Working Paper |
| Popis: | Let $W_{m|n}$ be the (finite) $W$-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb{C})$. In this paper we study the {\em Whittaker coinvariants functor}, which is an exact functor from category $\mathcal O$ for $\mathfrak{gl}_{m|n}(\mathbb{C})$ to a certain category of finite-dimensional modules over $W_{m|n}$. We show that this functor has properties similar to Soergel's functor $\mathbb V$ in the setting of category $\mathcal O$ for a semisimple Lie algebra. We also use it to compute the center of $W_{m|n}$ explicitly, and deduce some consequences for the classification of blocks of $\mathcal O$ up to Morita/derived equivalence. Comment: 58 pages, minor changes |
| Databáze: | arXiv |
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