On the structure of the category O for W-Algebras

Ivan Losev (1)

1 Department of Mathematics [MIT]

A W-algebra (of finite type) W is a certain associative algebra associated with a semisimple Lie algebra, say $g$, and its nilpotent element, say $e$. The goal of this paper is to study the category $O$ for $W$ introduced by Brundan, Goodwin and Kleshchev. We establish an equivalence of this category with a certain category of $g$-modules. In the case when $e$ is of principal Levi type (this is always so when $g$ is of type A) the category of $g$-modules in interest is the category of generalized Whittaker modules introduced by McDowell, and studied by Milicic-Soergel and Backelin.

Domaines: Théorie des représentations [math.RT]

Ivan Losev. On the structure of the category O for W-Algebras. 2008. ⟨hal-00441313⟩