A tale of parahoric--Hecke algebras, Bernstein and Satake homomorphisms
Abstract
Let G be a connected reductive group over a non-archimedean local field F. Let KF be the parahoric subgroup attached to a facet F in the Bruhat--Tits building of G. The ultimate goal of the present paper is to describe the center of the parahoric--Hecke algebra H(G(F)//KF, Z[q-1]) with level KF and prove the compatibility of generalized (twisted) Bernstein and Satake homomorphisms.
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