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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References
Görtz U.: On the flatness of models of certain Shimura varieties of PEL-type. Math. Ann. 321(3), 689–727 (2001)
Görtz U.: On the flatness of local models for the symplectic group. Adv. Math. 176(1), 89–115 (2003)
Görtz U.: Topological flatness of local models in the ramified case. Math. Z. 250(4), 775–790 (2005)
Haines T.J.: Test functions for Shimura varieties: the Drinfeld case. Duke Math. J. 106(1), 19–40 (2001)
Haines T.J., Ngô B.C.: Alcoves associated to special fibers of local models. Am. J. Math. 124(6), 1125–1152 (2002)
Minuscule alcoves for GL n and GSp 2n . Manuscripta Math. 102(4), 403–428 (2000)
Pappas G., Rapoport M.: Local models in the ramified case: II. Splitting models. Duke Math. J. 127(2), 193–250 (2005)
Pappas G., Rapoport M.: Local models in the ramified case: III. Unitary groups. J. Inst. Math. Jussieu 8(3), 507–564 (2009)
Rapoport M.: A guide to the reduction modulo p of Shimura varieties. Astérisque 298, 271–318 (2005)
Rapoport, M., Zink, Th.: Period spaces for p-divisible groups. In: Annals of Mathematics Studies, vol. 141, Princeton University Press, Princeton, NJ (1996)
Smithling B.D.: Topological flatness of local models for ramified unitary groups: I. The odd dimensional case. Adv. Math. 226, 3160–3190 (2011)
Smithling, B.D.: Topological flatness of orthogonal local models in the split, even case: I. Math. Ann. (To appear)
Smithling, B.D.: Topological flatness of local models for ramified unitary groups: II. The even dimensional case (in preparation)
Steinberg, R.: Endomorphisms of linear algebraic groups. In: Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, RI (1968)
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Smithling, B.D. Admissibility and permissibility for minuscule cocharacters in orthogonal groups. manuscripta math. 136, 295–314 (2011). https://doi.org/10.1007/s00229-011-0439-8
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DOI: https://doi.org/10.1007/s00229-011-0439-8