On semisimple l-modular Bernstein-blocks of a p-adic general linear group

2011/12/07 by David-Alexandre Guiraud, Guiraud, David-Alexandre
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1112.1567

openalex publication_date 2011/12/07 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Let G_n=GL_n(F), where F is a non-archimedean local field with residue characteristic p. Our starting point is the Bernstein-decomposition of the representation category of G_n over an algebraically closed field of characteristic ℓ ≠ p into blocks. In level zero, we associate to each block a replacement for the Iwahori-Hecke algebra which provides a Morita-equivalence just as in the complex case. Additionally, we will explain how this gives rise to a description of an arbitrary G_n-block in terms of simple G_m-blocks (for m≤ n), paralleling the approach of Bushnell and Kutzko in the complex setting.

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