Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Francesco Lemma
Email des responsables : alexis.bouthier@imj-prg.fr, francesco.lemma(at)imj-prg.fr
Salle :
Adresse :

Orateur(s) Lucas Mason-Brown - University of Oxford,
Titre Arthur packets over R and parabolic induction
Horaire10:30 à 12:00

Let G(R) be the real points of a connected reductive algebraic group with L-group G^L. For each Arthur parameter W_R \times SL(2) \to G^L, there is an associated "Arthur packet" of irreducible admissible G(R)-representations satisfying various desiderata. It is conjectured that all such representations are unitary (this is a theorem due to Arthur for quasisplit classical groups). An Arthur parameter is said to be "distinguished unipotent" if its restriction to C* \subset W_R is trivial and the image of the SL(2) is not contained in a proper Levi subgroup. In this talk, I will show that every Arthur packet can be built in a systematic way (through real parabolic and cohomological induction) from a distinguished unipotent Arthur packet. This reduces the question of unitarity to the case of unipotent distinguished parameters (and settles the question of unitarity for parameters which are "principal in a Levi"). This is joint work in progress with David Vogan and Jeffrey Adams.

AdresseSophie Germain