| Abstrakt: |
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 Jolissaint (J K-Theory 2:723-735, ; Trans Amer Math Soc 317(1):167-196, ) 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-groups. [ABSTRACT FROM AUTHOR] |
Full text from SpringerLink