University of Massachusetts Amherst
	Department of Mathematics and Statistics
	Representation Theory

Abstract: Let k and F_q be an algebraically closed and a finite field of characteristic 2 respectively. Let G be an adjoint (resp. simply connected) algebraic group of type B,C or D over k, g the Lie algebra of G and g^* the dual vector space of g. We construct the Springer correspondence for g (resp. g^*) following Lusztig's method. The correspondence is a bijective map from the set A_g (resp. A_g^*) to the set of irreducible characters of the Weyl group of G, where A_g (resp. A_g^*) is the set of all pairs (c,F) with c a nilpotent G-orbit in g (resp. g^*) and F an irreducible G-equivariant local system on c (up to isomorphism). In particular, we obtain classifications of nilpotent orbits in orthogonal Lie algebras over F_q and in the duals of classical Lie algebras over k and F_q. Finally, we describe the explicit correspondence using similar combinatorics that appears in the description of generalized Springer correspondence (defined by Lusztig) for classical groups in the case of characteristic not equal 2 and unipotent case in characteristic 2.