Simon Goodwin Finite dimensional irreducible modules for finite W-algebras associated to even multiplicity nilpotents in classical Lie algebras (joint with Jonathan Brown) Let \g be the Lie algebra \sp_{2n}(\C) or \so_{2n}(\C) and let e \in \g be a nilpotent element for which all parts of its Jordan decomposition have even multiplicity. The finite W-algebra algebra U(\g,e) associated to e is a certain finitely generated algebra obtained from the universal enveloping algebra U(\g) of \g by a certain quantum Hamiltonian reduction. I will describe a combinatorial classification of the finite dimensional irreducible U(\g,e)-modules based on the highest weight theory for finite W-algebras developed by Brundan--G--Kleshchev. Using results of Premet and Losev, this leads to a parameterization of the primitive ideals of U(\g) with associated variety the closure of the nilpotent orbit of e.