Journal of Lie Theory 28 (2018), No. 2, 323--341
Copyright Heldermann Verlag 2018
The Orbit Method for the Baum-Connes Conjecture for Algebraic Groups over Local Function Fields
Siegfried Echterhoff
Mathematisches Institut, WWU Münster, Einsteinstrasse 62, 48149 Münster, Germany
echters@uni-muenster.de
Kang Li
Mathematisches Institut, WWU Münster, Einsteinstrasse 62, 48149 Münster, Germany
lik@uni-muenster.de
Ryszard Nest
Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
rnest@math.ku.dk
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 [see J. Chabert, S. Echterhoff, and R. Nest, The Connes-Kasparov conjecture for almost connected groups and for linear p-adic groups, Publ. Math. Inst. Hautes Etudes Sci. 97 (2003) 239--278] 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.
Keywords: Orbit method, Baum-Connes conjecture, linear algebraic groups, local function fields.
MSC: 19K35, 20G25
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