On the Structure of the Category O for W-algebras
نویسنده
چکیده
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 categoryO 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.
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