Geodesic
Harish-Chandra's Schwartz Algebras Associated with Discrete Subgroups of Semisimple Lie Groups
Adrien Boyer1
1Faculty of Mathematics, The Weizmann Institute of Science, Herzl Street 234, Rehovot, Israel
Journal of Lie Theory, Tome 27 (2017) no. 3, pp. 831-844

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove that the Harish-Chandra's Schwartz space associated with a discrete subgroup of a semisimple Lie group is a dense subalgebra of the reduced C*-algebra of the discrete subgroup. Then, we prove that the reduced C*-norm is controlled by the norm of the Harish-Chandra's Schwartz space. This inequality is weaker than property RD and holds for any discrete group acting isometrically, properly on a Riemannian symmetric space.
Classification : 46H15, 43A90, 22E40, 22D20, 22D25, 46L80
Mots-clés : Harish-Chandra's Schwartz spaces, semisimple Lie groups, Harish-Chandra functions, Furstenberg boundary, property RD, K-theory, Baum-Connes conjecture

Adrien Boyer  1

1 Faculty of Mathematics, The Weizmann Institute of Science, Herzl Street 234, Rehovot, Israel 
Adrien Boyer. Harish-Chandra's Schwartz Algebras Associated with Discrete Subgroups of Semisimple Lie Groups. Journal of Lie Theory, Tome 27 (2017) no. 3, pp. 831-844. http://geodesic.mathdoc.fr/item/JOLT_2017_27_3_a9/
@article{JOLT_2017_27_3_a9,
     author = {Adrien Boyer},
     title = {Harish-Chandra's {Schwartz} {Algebras} {Associated} with {Discrete} {Subgroups} of {Semisimple} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {831--844},
     year = {2017},
     volume = {27},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_3_a9/}
}
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