Algebra & Number Theory

Blocks of the category of smooth $\ell$-modular representations of GL$(n,F)$ and its inner forms: reduction to level 0

Gianmarco Chinello

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Abstract

Let G be an inner form of a general linear group over a nonarchimedean locally compact field of residue characteristic p, let R be an algebraically closed field of characteristic different from p and let R(G) be the category of smooth representations of G over R. In this paper, we prove that a block (indecomposable summand) of R(G) is equivalent to a level-0 block (a block in which every simple object has nonzero invariant vectors for the pro-p-radical of a maximal compact open subgroup) of R(G), where G is a direct product of groups of the same type of G.

Article information

Source
Algebra Number Theory, Volume 12, Number 7 (2018), 1675-1713.

Dates
Received: 31 July 2017
Revised: 8 May 2018
Accepted: 12 June 2018
First available in Project Euclid: 9 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.ant/1541732438

Digital Object Identifier
doi:10.2140/ant.2018.12.1675

Mathematical Reviews number (MathSciNet)
MR3871507

Zentralblatt MATH identifier
06976299

Subjects
Primary: 20C20: Modular representations and characters
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Keywords
equivalence of categories blocks modular representations of p-adic reductive groups type theory semisimple types Hecke algebras level-0 representations

Citation

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


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