An inverse Satake isomorphism in characteristic p

2012/07/23 by Rachel Ollivier, Ollivier, Rachel
Mathematics · #20C08 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:20C08 #msc:22E50

paper · pdf · doi:10.48550/arxiv.1207.5557

arxiv created 2012/07/23 · arxiv updated 2012/07/25

Abstract

Let F be a local field with finite residue field of characteristic p and k an algebraic closure of the residue field. Let G be the group of F-points of a F-split connected reductive group. In the apartment corresponding to a chosen maximal split torus of T, we fix a hyperspecial vertex and denote by K the corresponding maximal compact subgroup of G. Given an irreducible smooth k-representation ρ of K, we construct an isomorphism from the affine semigroup k-algebra of the dominant cocharacters of T onto the Hecke algebra H(G, ρ). In the case when the derived subgroup of G is simply connected, we prove furthermore that our isomorphism is the inverse to the Satake isomorphism constructed by Herzig.

Related

• The Satake isomorphism for special maximal parahoric Hecke algebras
• Determining a connected split reductive group from its irreducible representations
• On the Satake isomorphism
• Parahoric Hecke Ext-algebras in characteristic p
• Structure of Hecke algebras arising from types