Block decomposition of the category of l-modular smooth representations of GL(n,F) and its inner forms

Vincent Sécherre, Shaun Stevens

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
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Abstract

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.
Original languageEnglish
Pages (from-to)669-709
Number of pages41
JournalAnnales Scientifiques de l’École Normale Supérieure
Volume49
Issue number3
DOIs
Publication statusPublished - 2016

Keywords

  • Modular representations of p-adic reductive groups
  • semisimple types
  • Inertial classes
  • supercuspidal support
  • blocks

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