Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 7 (2018), 1675-1713.
Blocks of the category of smooth $\ell$-modular representations of GL$(n,F)$ and its inner forms: reduction to level 0
Let be an inner form of a general linear group over a nonarchimedean locally compact field of residue characteristic , let be an algebraically closed field of characteristic different from and let be the category of smooth representations of over . In this paper, we prove that a block (indecomposable summand) of is equivalent to a level- block (a block in which every simple object has nonzero invariant vectors for the pro--radical of a maximal compact open subgroup) of , where is a direct product of groups of the same type of .
Algebra Number Theory, Volume 12, Number 7 (2018), 1675-1713.
Received: 31 July 2017
Revised: 8 May 2018
Accepted: 12 June 2018
First available in Project Euclid: 9 November 2018
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Chinello, Gianmarco. Blocks of the category of smooth $\ell$-modular representations of GL$(n,F)$ and its inner forms: reduction to level 0. Algebra Number Theory 12 (2018), no. 7, 1675--1713. doi:10.2140/ant.2018.12.1675. https://projecteuclid.org/euclid.ant/1541732438