Journal of Lie Theory

no. 3
Harish-Chandra's Schwartz Algebras Associated with Discrete Subgroups of Semisimple Lie Groups
Journal of Lie Theory, Volume 27 (2017) no. 3, pp. 831-844
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.
DOI: 10.5802/jolt.971
Classification: 46H15, 43A90, 22E40, 22D20, 22D25, 46L80
Keywords: Harish-Chandra's Schwartz spaces, semisimple Lie groups, Harish-Chandra functions, Furstenberg boundary, property RD, K-theory, Baum-Connes conjecture 
@article{JOLT_2017_27_3_a9,
     author = {A. 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},
     doi = {10.5802/jolt.971},
     zbl = {1404.22016},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.971/}
}
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A. Boyer. Harish-Chandra's Schwartz Algebras Associated with Discrete Subgroups of Semisimple Lie Groups. Journal of Lie Theory, Volume 27 (2017) no. 3, pp. 831-844. doi: 10.5802/jolt.971

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