The orbit method for the Baum-Connes Conjecture for algebraic groups over local function fields
K-Theory and Homology
2019-02-21 v1
Abstract
The main purpose of this paper is to modify the orbit method for the Baum-Connes conjecture as developed by Chabert, Echterhoff and Nest in their proof of the Connes-Kasparov conjecture for almost connected groups \cite{MR2010742} in order to deal with linear algebraic groups over local function fields (i.e., non-archimedean local fields of positive characteristic). As a consequence, we verify the Baum-Connes conjecture for certain Levi-decomposable linear algebraic groups over local function fields. One of these is the Jacobi group, which is the semidirect product of the symplectic group and the Heisenberg group.
Cite
@article{arxiv.1704.08548,
title = {The orbit method for the Baum-Connes Conjecture for algebraic groups over local function fields},
author = {Siegfried Echterhoff and Kang Li and Ryszard Nest},
journal= {arXiv preprint arXiv:1704.08548},
year = {2019}
}