Parabolic restriction of tempered representations
Tyrone Crisp (MPI Bonn)
Tuesday 10th November, 2015 16:00-17:00 Maths 522
Parabolic induction is a procedure for building representations of a reductive group from representations of a Levi subgroup. It plays an important role in the representation theory of both real and p-adic groups. For smooth representations of p-adic groups, parabolic induction admits an obvious left-adjoint restriction functor (the Jacquet functor) which, by a remarkable theorem of Bernstein, is also a right adjoint. I will present partial analogues of this "second adjoint theorem" for real groups, in various categories of representations: Hilbert modules, operator modules, and modules over Harish-Chandra's Schwartz algebra.
This is based on joint work with Pierre Clare, Nigel Higson and Robert Yuncken.