Abstract
For a given cocharacter μ, μ-admissibility and μ-permissibility are combinatorial notions introduced by Kottwitz and Rapoport that arise in the theory of bad reduction of Shimura varieties. In this paper we prove that μ-admissibility is equivalent to μ-permissibility in all previously unknown cases of minuscule cocharacters μ in Iwahori–Weyl groups attached to split orthogonal groups. This, combined with other cases treated previously by Kottwitz–Rapoport and the author, establishes the equivalence of μ-admissibility and μ-permissibility for all minuscule cocharacters in split classical groups, as conjectured by Rapoport.
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