A Satake homomorphism for the \bmod p derived Hecke algebra

2018/08/20 by Ronchetti, Niccolò
#11F06 #11F33 #11F70 #11F75 #11F85 #20C08 #22E41 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1808.06512

Abstract

We explore the structure of the derived spherical Hecke algebra of a p-adic group, a graded associative algebra whose degree 0 subalgebra is the classical spherical Hecke algebra. Working with \mathbb Z/ p^a coefficients, we establish a Satake homomorphism relating this graded algebra to the corresponding graded algebra for the torus. We investigate the image of this homomorphism in degree 1, as well as other properties, such as transitivity with respect to inclusion of Levi subgroups.

Related

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• Iwahori-Hecke algebras for p-adic loop groups
• Derived Satake morphisms for p-small weights in characteristic p
• Geometrization of the Satake transform for mod p Hecke algebras
• On the Satake isomorphism