Minuscule alcoves for GLn and GSp2n

Abstract:

Let μ be a minuscule coweight for either GL _n or GSp _2n , and regard μ as an element t _μ in the extended affine Weyl group . We say that an element is μ-admissible if there exists μ′ in the Weyl group orbit of μ such that x≤t _μ′ in the Bruhat order on . Our main result is that is μ-admissible if and only if it is μ-permissible, where μ-permissibility is defined using inequalities arising naturally in the study of bad reduction of Shimura varieties.