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

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

2011-12-07

arxiv.org/abs/1112.1567v1

Mathematics

Representation Theory

Scientific paper

Let $G_n=\operatorname{GL}_n(F)$, 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 $\ell \neq p$ 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 $m\leq n$), paralleling the approach of Bushnell and Kutzko in the complex setting.

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