Constant term functors with \mathbbF_p-coefficients

2021/07/01 by Robert Cass, Cass, Robert, Cédric Pépin +1
Mathematics · #14F10 #14M15 #20C08 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.AG #math.NT #math.RT #msc:14F10 #msc:14M15 #msc:20C08

paper · pdf · doi:10.48550/arxiv.2107.00714

47 pages

arxiv created 2021/07/01 · arxiv updated 2021/07/05

Abstract

We study the constant term functor for \mathbbF_p-sheaves on the affine Grassmannian in characteristic p with respect to a Levi subgroup. Our main result is that the constant term functor induces a tensor functor between categories of equivariant perverse \mathbbF_p-sheaves. We apply this fact to get information about the Tannakian monoids of the corresponding categories of perverse sheaves. As a byproduct we also obtain geometric proofs of several results due to Herzig on the mod p Satake transform and the structure of the space of mod p Satake parameters.

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