Admissibility and permissibility for minuscule cocharacters in orthogonal groups

摘要

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.