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Unramified ℓ-modular representations of GLn(F) and its inner forms


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Opened Access Unramified ℓ-modular representations of GLn(F) and its inner forms

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Author: Mínguez Espallargas, Alberto
Sécherre, Vincent
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2014
Published in: International Mathematics Research Notices, 2014 (8), 2090-2118.
Document type: Article
Abstract: Let F be a non-Archimedean locally compact field of residue characteristic p and R be an algebraically closed field of characteristic l different from p. Let G be the group GLn, n ¥ 1, over F or one of its inner forms. In this article, we prove that the unramified irreducible smooth R-representations of G(F) are those representations that are irreducibly induced from an unramified character of a Levi subgroup. We deduce that any irreducible unramified Fl-representation of G(F) can be lifted to Ql, which proves a conjecture by Vignéras.
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DOI: 10.1093/imrn/rns278

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