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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.
|Number of pages||41|
|Journal||Annales Scientifiques de l’École Normale Supérieure|
|Publication status||Published - 2016|
- Modular representations of p-adic reductive groups
- semisimple types
- Inertial classes
- supercuspidal support
- School of Mathematics - Professor of Mathematics
- Algebra and Combinatorics - Member
Person: Research Group Member, Academic, Teaching & Research
- 1 Finished
Explicit Correspondences in Number Theory.
Engineering and Physical Sciences Research Council
31/03/10 → 30/03/15