Hecke module structure on first and top pro-p-Iwahori cohomology

2017/08/09 by Karol Koziol, Koziol, Karol
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1708.03013

17 pages. Added result about Poincare duality along with other minor changes. To appear in Acta Arithmetica

arxiv created 2018/03/24 · arxiv updated 2018/03/28

Abstract

Let p≥ 5 be a prime number, G a split connected reductive group defined over a p-adic field, and I₁ a choice of pro-p-Iwahori subgroup. Let C be an algebraically closed field of characteristic p and H the pro-p-Iwahori--Hecke algebra over C associated to I₁. In this note, we compute the action of H on \textrmH¹(I₁,C) and \textrmH^\textrmtop(I₁,C) when the root system of G is irreducible. We also give some partial results in the general case.

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