Alcoves associated to special fibers of local models
Haines, T. · Ngo, B. C.
Original · EN
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. Also, we recover a theorem of Deodhar characterizing the Bruhat order on Sₙ.
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