Décomposition en blocs de la catégorie des représentations lisses ℓ-modulaires de GLn(F) et de ses formes intérieures
| Autor: | Shaun Stevens, Vincent Sécherre |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques de Versailles (LMV), Université Paris-Saclay-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS), School of mathemtaics - University fo East Anglia (UEA), University of East Anglia [Norwich] (UEA), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Pure mathematics
General Mathematics es inertielles 01 natural sciences Modular representations of p-adic reductive groups 0103 physical sciences FOS: Mathematics Partition (number theory) Locally compact space 0101 mathematics Algebraically closed field Representation Theory (math.RT) 2010 MSC: 22E50 Semisimple types Mathematics::Representation Theory Représentations modulaires des groupes réductifs p-adiques Mathematics Subcategory Supercuspidal support [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] 010102 general mathematics blocs 16. Peace & justice support supercuspidal 22E50 Blocks Inertial classes Irreducible representation types semi-simples 010307 mathematical physics Indecomposable module Mathematics - Representation Theory |
| Zdroj: | Annales Scientifiques de l'École Normale Supérieure Annales Scientifiques de l'École Normale Supérieure, Société mathématique de France, 2016, 49 (3), pp.669-709. ⟨10.24033/asens.2293⟩ |
| ISSN: | 0012-9593 1873-2151 |
| DOI: | 10.24033/asens.2293⟩ |
| Popis: | 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. To any irreducible smooth representation of G=GL(m,D) with coefficients in R, we can attach a uniquely determined inertial class of supercuspidal pairs of G. This provides us with a partition of the set of all isomorphism classes of irreducible representations of G. We write R(G) for the category of all smooth representations of G with coefficients in R. To any inertial class O of supercuspidal pairs of G, we can attach the subcategory R(O) made of smooth representations all of whose irreducible subquotients are in the subset determined by this inertial class. We prove that R(G) decomposes into the product of the R(O), where O ranges over all possible inertial class of supercuspidal pairs of G, and that each summand R(O) is indecomposable. 37 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|