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

2016/07/26 by Adrien Boyer, Boyer, Adrien
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1607.07830

openalex publication_date 2016/07/26 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We prove that the Harish-Chandra--Schwartz space associated with a discrete\nsubgroup of a semisimple Lie group is a dense subalgebra of the reduced\nC^*-algebra of the discrete subgroup. Then, we prove that for the reduced\nC^*-norm is controlled by the norm of the Harish-Chandra--Schwartz space.\nThis inequality is weaker than property RD and holds for any discrete group\nacting isometrically, properly on a Riemannian symmetric space.\n

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