AN EXOTIC DELIGNE-LANGLANDS CORRESPONDENCE FOR SYMPLECTIC GROUPS

Let G = Sp(2n, C) be a complex symplectic group. We introduce a (G x (Cx)(l+1))-veriety N-e which we call the l-exotic nilpotent cone. Then, we realize the Hecke algebra H of type C-n((1)) with three parameters via equivariant algebraic K-theory in terms of the geometry of N-2. This enables its to establish a Deligne-Langlands-type classification of simple H-modules under a mild assumption on parameters. As applications, the present a character formula and multiplicity formulas of H-modules.