Conjectures about padic groups and their noncommutative geometry
Abstract
Let G be any reductive padic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G. At the heart of these conjectures are statements about the geometric structure of Bernstein components for G, both at the level of the space of irreducible representations and at the level of the associated Hecke algebras. We relate this to two wellknown conjectures: the local Langlands correspondence and the BaumConnes conjecture for G. In particular, we present a strategy to reduce the local Langlands correspondence for irreducible Grepresentations to the local Langlands correspondence for supercuspidal representations of Levi subgroups.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.02837
 Bibcode:
 2015arXiv150802837A
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  KTheory and Homology;
 20G25;
 22E50;
 11S37;
 19L47
 EPrint:
 V2: several small corrections, in particular an improved definition of the component group $S_\phi$