  Let V be a 2n dimensional vector space over an algebraically closed field of
odd characteristic. Let G = GL(V) and H = Sp_{2n} be the symplectic group
contained in G. We call X = G/H \times V the exotic symmetric space, since its
"unipotent" part is isomorphic to Kato's exotic nilcone. Let W be the Weyl
group of type C_n. Kato established the Springer correspondence between
irreducible characters of W and H-orbits in the exotic nilcone, based on the
Ginzburg theory of affine Hecke algebras. In this paper, we develpoe a theory
of character sheaves on X, and give an alternate proof for the Springer
correspondence based on the theroy of character sheaves.
