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Admissibility and permissibility for minuscule cocharacters in orthogonal groups. (English) Zbl 1229.05290
Summary: For a given cocharacter \(\mu\), \(\mu\)-admissibility and \(\mu\)-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 \(\mu\)-admissibility is equivalent to \(\mu\)-permissibility in all previously unknown cases of minuscule cocharacters \(\mu\) 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 \(\mu\)-admissibility and \(\mu\)-permissibility for all minuscule cocharacters in split classical groups, as conjectured by Rapoport.

MSC:
05E15 Combinatorial aspects of groups and algebras (MSC2010)
14G35 Modular and Shimura varieties
17B22 Root systems
20G15 Linear algebraic groups over arbitrary fields
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