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Abstract: Suppose that G is a connected reductive group over a p-adic field F, that Kis a hyperspecial maximal compact subgroup of GF, and that V is anirreducible representation of K over the algebraic closure of the residue fieldof F. We establish an analogue of the Satake isomorphism for the Hecke algebraof compactly supported, K-biequivariant functions f: GF \to End V. TheseHecke algebras were first considered by Barthel-Livne for GL 2. They play arole in the recent mod p and p-adic Langlands correspondences for GL 2Q p, ingeneralisations of Serre-s conjecture on the modularity of mod p Galoisrepresentations, and in the classification of irreducible mod p representationsof unramified p-adic reductive groups.



Author: Florian Herzig

Source: https://arxiv.org/







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