Number Theory Seminar

I will report on a joint project with Ahmed Moussaoui and Maarten Solleveld. We introduced notions of cuspidality and cuspidal support for enhanced L-parameters of reductive p-adic groups. We obtained a partition of the set of enhanced parameters that is modeled upon the Bernstein decomposition of the smooth dual of the p-adic group.

On the other hand, in the case of classical groups, works of Arthur and Moeglin allow to attach, via twisted endoscopy, a cuspidal enhanced L-parameter to each irreducible supercuspidal representation. Focusing on examples, we will show that there exists an isomorphism between the Hecke algebras associated to the corresponding Bernstein blocks which coincides with the Langlands correspondence constructed by Arthur.