Représentations lisses modulo l de GL(m,D)

Alberto Minguez (1) , Vincent Sécherre (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 LMV - Laboratoire de Mathématiques de Versailles

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. We classify all smooth irreducible representations of GL(m,D) with coefficients in R, in terms of multisegments, generalizing works by Zelevinski, Tadic and Vignéras. We prove that any irreducible R-representation of GL(m,D) has a unique supercuspidal support, and thus get two classifications: one by supercuspidal multisegments, classifying representations with a given supercuspidal support, and one by aperiodic multisegments, classifying representations with a given cuspidal support. These constructions are made in a purely local way, with a substantial use of type theory.

Domaines: Théorie des représentations [math.RT]

Alberto Minguez, Vincent Sécherre. Représentations lisses modulo l de GL(m,D). Duke Mathematical Journal, 2014, 163 (4). ⟨hal-00630047v2⟩