Alcoves associated to special fibers of local models
Representation Theory
2007-05-23 v1 Algebraic Geometry
Combinatorics
Abstract
The special fiber of the local model of a PEL Shimura variety with Iwahori-type level structure admits a cellular decomposition. The set of strata is in a natural way a finite subset of the affine Weyl group determined by the Shimura data. In this paper, we generalize and give a new proof of a theorem of Kottwitz and Rapoport concerning the description of this set for the case of linear and symplectic groups. For higher rank groups not of type A_n, we produce counterexamples showing the situation is not as nice in general. Also, we recover a theorem of Deodhar characterizing the Bruhat order on S_n.
Keywords
Cite
@article{arxiv.math/0103048,
title = {Alcoves associated to special fibers of local models},
author = {T. Haines and B. C. Ngo},
journal= {arXiv preprint arXiv:math/0103048},
year = {2007}
}
Comments
3 figures