Representation theory of standard Levi classical finite W algebras

Let U(g,e) denote a finite W-algebra, where g is a reductive classical Lie algebra and e is a nilpotent element of g. In this talk I will give a classification of the finite dimensional irreducible U(g,e)-modules in the case that e is of standard Levi type. The classification follows from conjecture of Brundan, Goodwin, and Kleshchev (which was proved by Losev), which allows one to reduce the problem of classifying finite dimensional irreducible U(g,e)-modules when e is of standard Levi type in g to finding the associated variety of certain highest weight modules for reductive Lie algebras. This work is joint with Simon Goodwin.