Journal of Lie Theory

no. 2
The Orbit Method for the Baum-Connes Conjecture for Algebraic Groups over Local Function Fields
Siegfried Echterhoff1; Kang Li1; Ryszard Nest2
1Mathematisches Institut, WWU Münster, Einsteinstrasse 62, 48149 Münster, Germany
2Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 323-341
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.
DOI: 10.5802/jolt.1004
Classification: 19K35, 20G25
Keywords: Orbit method, Baum-Connes conjecture, linear algebraic groups, local function fields

Siegfried Echterhoff  1 ; Kang Li  1 ; Ryszard Nest  2

1 Mathematisches Institut, WWU Münster, Einsteinstrasse 62, 48149 Münster, Germany
2 Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark 
Siegfried Echterhoff; Kang Li; Ryszard Nest. The Orbit Method for the Baum-Connes Conjecture for Algebraic Groups over Local Function Fields. Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 323-341. doi: 10.5802/jolt.1004
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