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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.

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