Orateur
Robert Yuncken
Description
Harish-Chandra spent his career understanding the unitary representations of real reductive Lie groups like SL(n,R). One of the crucial points in this theory is his "philosophy of cusp forms", which says that any tempered unitary representation of a real reductive group (with compact centre) is either discrete series, meaning it is a subrepresentation of the regular representation, or it is induced from a parabolic subgroup, such as the block upper-triangular subgroup in SL(n,R). This sets up an inductive argument over ever smaller subgroups. I will describe how Harish-Chandra’s principal follows from a Lie groupoid construction due to Omar Mohsen plus some C*-algebra theory.
(Joint work with Jacob Bradd and Nigel Higson)
