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  • Author: Marie-France Vignéras x
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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 B=ZU. 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 (G,K,V) for the intertwining Hecke algebra of V in G, we define a natural algebra homomorphism from (G,K,V) to (Z,ZK,VUK), 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 𝔽p. We show that in the general case (G,K,V) 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.