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A Satake isomorphism for representations modulo p of reductive groups over local fields.
- Source :
- Journal für die Reine und Angewandte Mathematik; Apr2015, Vol. 2015 Issue 701, p33-75, 43p
- Publication Year :
- 2015
-
Abstract
- Let F be a local field with finite residue field of characteristic p. Let G be a connected reductive group over F and B a minimal parabolic subgroup of G with Levi decomposition . Let K be a special parahoric subgroup of G, in good position relative to ( Z, U). Fix an absolutely irreducible smooth representation of K on a vector space V over some field C of characteristic p. Writing for the intertwining Hecke algebra of V in G, we define a natural algebra homomorphism from to , we show it is injective and identify its image. We thus generalize work of F. Herzig, who assumed F of characteristic 0, G unramified and K hyperspecial, and took for C an algebraic closure of the prime field 픽<subscript> p</subscript>. We show that in the general case need not be commutative; that is in contrast with the cases Herzig considers and with the more classical situation where V is trivial and the field of coefficients is the field of complex numbers. [ABSTRACT FROM AUTHOR]
- Subjects :
- ISOMORPHISM (Mathematics)
FINITE fields
BOREL subgroups
VECTOR spaces
HOMOMORPHISMS
Subjects
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2015
- Issue :
- 701
- Database :
- Complementary Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 101894690
- Full Text :
- https://doi.org/10.1515/crelle-2013-0021