Alcoves associated to special fibers of local models

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 An, we produce counterexamples showing the situation is not as nice in general. We also recover a theorem of Deodhar characterizing the Bruhat order on Sn. 1. Introduction. Let G be a classical group over the p-adic field Qp, and let µ be a dominant minuscule coweight of G. We assume that the pair (G,µ) comes from a PEL-type Shimura datum (G, X, K) where the p-component Kp of the compact open subgroup K is an Iwahori subgroup of G(Qp) = G(Qp). We assume that the corresponding Shimura variety Sh (G, X, K) has a model over