Exotic symmetric space over a finite field, I
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 \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.
Keywords
Cite
@article{arxiv.1207.5093,
title = {Exotic symmetric space over a finite field, I},
author = {Toshiaki Shoji and Karine Sorlin},
journal= {arXiv preprint arXiv:1207.5093},
year = {2013}
}
Comments
56 pages, the proof of Proposition 4.8 revised, and typos corrected. The results unchanged