Unramified -modular representations of GLn(F) and its inner forms
Résumé
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 GL(n) over F or one of its inner forms. In this article, we classify the unramified irreducible smooth R-representations of G(F): more precisely we prove that they are those representations that are irreducibly induced from an unramified character of a Levi subgroup. We deduce that any smooth irreducible unramified mod ℓ representation of G(F) can be lifted to an ℓ-adic representation, which proves a conjecture by Vignéras.
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