Emmy-Noether-Seminar: "Kirillov's orbit method for the Baum-Connes conjecture for algebraic groups"
Kirillov’s orbit method for the Baum-Connes conjecture for algebraic groups
Abstract: The orbit method for the Baum-Connes conjecture was first developed by Chabert and Echterhoff in the study of permanence properties for the Baum Connes conjecture. Together with Nest they were able to apply the orbit method to verify the conjecture for almost connected groups and p-adic groups.
In this talk, we will discuss how to prove the Baum-Connes conjecture for linear algebraic groups over local fields of positive characteristic along the same idea. It turns out that the unitary representation theory of unipotent groups plays an essential role in the proof. As an example, we will concentrate on the Jacobi group, which is the semi-direct product of the symplectic group with the Heisenberg group. It is well-known that the Jacobi group has Kazhdans property (T), which is an obstacle to prove the Baum-Connes conjecture. If time permits, we will also discuss my recent joint work with Maarten Solleveld about quasi-reductive groups.