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.
Classification :
19K35, 20G25
Mots-clés :
Orbit method, Baum-Connes conjecture, linear algebraic groups, local function fields
Affiliations des auteurs :
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, Tome 28 (2018) no. 2, pp. 323-341. http://geodesic.mathdoc.fr/item/JOLT_2018_28_2_a1/
@article{JOLT_2018_28_2_a1,
author = {Siegfried Echterhoff and Kang Li and Ryszard Nest},
title = {The {Orbit} {Method} for the {Baum-Connes} {Conjecture} for {Algebraic} {Groups} over {Local} {Function} {Fields}},
journal = {Journal of Lie Theory},
pages = {323--341},
year = {2018},
volume = {28},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2018_28_2_a1/}
}
TY - JOUR
AU - Siegfried Echterhoff
AU - Kang Li
AU - Ryszard Nest
TI - The Orbit Method for the Baum-Connes Conjecture for Algebraic Groups over Local Function Fields
JO - Journal of Lie Theory
PY - 2018
SP - 323
EP - 341
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2018_28_2_a1/
ID - JOLT_2018_28_2_a1
ER -
%0 Journal Article
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%A Kang Li
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%T The Orbit Method for the Baum-Connes Conjecture for Algebraic Groups over Local Function Fields
%J Journal of Lie Theory
%D 2018
%P 323-341
%V 28
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2018_28_2_a1/
%F JOLT_2018_28_2_a1
