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

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 positive 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 as in the complex case. Additionally, we explain how this gives rise to a description of an arbitrary G n -block in terms of simple G m -blocks (for m ⩽ n ), parallelling the approach of Bushnell and Kutzko in the complex setting.