Exotic symmetric space over a finite field, I

2012/07/21 by Shoji, Toshiaki, Sorlin, Karine
#20G05 #20G40 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1207.5093

Abstract

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 × 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.

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