Property (RD) for Hecke pairs

Details Property (RD) for Hecke pairs Property (RD) for Hecke pairs

2012-03-28

arxiv.org/abs/1203.6308v1

Mathematics

Operator Algebras

16 pages. This article has been submitted to a journal. So, its final version will appear later

Scientific paper

As the first step towards developing noncommutative geometry over Hecke C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989 to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C*-algebra. Hence they have the same K_0-groups.

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