Admissibility and permissibility for minuscule cocharacters in orthogonal groups

Details Admissibility and permissibility for minuscule cocharacters in orthogonal groups Admissibility and permissibility for minuscule cocharacters in orthogonal groups

2010-01-06

arxiv.org/abs/1001.0937v3

Mathematics

Algebraic Geometry

16 pages. Minor revisions, some of which incorporate suggestions of the referee

Scientific paper

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.

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