The first pro-p-Iwahori cohomology of mod-p principal series for p-adic \textrmGL_n

2017/08/09 by Karol Kozioł, Koziol, Karol
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1708.03014

openalex publication_date 2017/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p≥ 3 be a prime number and F a p-adic field. Let I₁ denote the pro-p-Iwahori subgroup of \textrmGL_n(F), and H the pro-p-Iwahori--Hecke algebra of \textrmGL_n(F) with respect to I₁ (over a coefficient field of characteristic p). We compute the structure of \textrmH¹(I₁,π) as an H-module, where π is a mod-p principal series representation of \textrmGL_n(F). We also give some partial results about the structure of \textrmH¹(I₁,π) for a general split reductive group with irreducible root system.

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