Projects per year
Abstract
Let F be a nonArchimedean locally compact field of residue characteristic p, let D be a finite dimensional central division Falgebra 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 language  English 

Pages (fromto)  669709 
Number of pages  41 
Journal  Annales Scientifiques de l’École Normale Supérieure 
Volume  49 
Issue number  3 
DOIs  
Publication status  Published  2016 
Keywords
 Modular representations of padic reductive groups
 semisimple types
 Inertial classes
 supercuspidal support
 blocks
Profiles

Shaun Stevens
 School of Mathematics  Professor of Mathematics
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research
Projects
 1 Finished

Explicit Correspondences in Number Theory.
Engineering and Physical Sciences Research Council
31/03/10 → 30/03/15
Project: Fellowship