An exotic Springer correspondence for symplectic groups
Representation Theory
2008-01-27 v2 Algebraic Geometry
Abstract
This paper is a sequel to math.RT/0601155. Let G be a complex symplectic group. In math.RT/0601155, we constructed a certain G-variety N = N_1, which we call the (1-) exotic nilpotent cone. In this paper, we study the set of G-orbits of the variety N. It turns out that the variety N gives a variant of the Springer correspondence for the Weyl group of type C, but shares a similar flavor with that of type A case. (I.e. there appears no non-trivial local system and the correspondence is bijective.) As an application, we present one sufficient condition for the bijectivity of our exotic Deligne-Langlands correspondence [K1].
Cite
@article{arxiv.math/0607478,
title = {An exotic Springer correspondence for symplectic groups},
author = {Syu Kato},
journal= {arXiv preprint arXiv:math/0607478},
year = {2008}
}
Comments
v2; 16pp. title changed, Nov/07 version except for one reference, may be merged into next revision of math.RT/0601155