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arXiv:0812.1584 [math.RT]AbstractReferencesReviewsResources

On the structure of the category O for W-algebras

Ivan Losev

Published 2008-12-08, updated 2009-05-31Version 3

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.

Comments: 11 pages, v2 some gaps fixed, some proofs rewritten, Remark 5.4 added, v3 15 pages, some gaps fixed, a new section is added
Categories: math.RT
Subjects: 17B35
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