Harish-Chandra--Schwartz's algebras associated with discrete subgroups of Semisimple Lie groups

Adrien Boyer

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arXiv · 1607.07830

Harish-Chandra--Schwartz's algebras associated with discrete subgroups of Semisimple Lie groups

Adrien Boyer

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Abstract

We prove that the Harish-Chandra--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 for the reduced $C^*$-norm is controlled by the norm of the Harish-Chandra--Schwartz space. This inequality is weaker than property RD and holds for any discrete group acting isometrically, properly on a Riemannian symmetric space.

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BibTeX RIS

Adrien Boyer. 2016-07-26. Harish-Chandra--Schwartz's algebras associated with discrete subgroups of Semisimple Lie groups. https://arxiv.org/abs/1607.07830

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