On the structure of the category O for W-algebras

Details On the structure of the category O for W-algebras On the structure of the category O for W-algebras

2008-12-08

arxiv.org/abs/0812.1584v3

Mathematics

Representation Theory

11 pages, v2 some gaps fixed, some proofs rewritten, Remark 5.4 added, v3 15 pages, some gaps fixed, a new section is added

Scientific paper

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 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 McDowel and studied by Milicic-Soergel and Backelin.

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