Block decomposition of the category of lmodular smooth representations of GL(n,F) and its inner forms
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.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5349
 Bibcode:
 2014arXiv1402.5349S
 Keywords:

 Mathematics  Representation Theory;
 22E50
 EPrint:
 37 pages