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Journal of Lie Theory 18 (2008), No. 3, 627--644
Copyright Heldermann Verlag 2008

The Constants of Cowling and Haagerup

Varadharajan Muruganandam
Dept. of Mathematics, Pondicherry University, Pondicherry 605 014, India


We give a simpler proof of the main theorem of M. Cowling and U. Haagerup ["Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one", Invent. Math. 96 (1989) 507--549], which reads as follows. Let $G$ be a connected real Lie group of real rank $1$ with finite centre. If $G$ is locally isomorphic to SO$_0(1,n)$ or SU$(1,n)$, then $\Lambda_G = 1$. If $G$ is locally isomorphic to Sp$(1,n)$, then $\Lambda_G = 2n-1$, while if $G$ is the exceptional rank one group $F_{4(-20)}$, then $\Lambda_G = 21$.

Keywords: Fourier algebra, weak amenability, Gelfand pair, hypergroup.

MSC: 43A30, 22D25, 43A62, 43A90, 43A22

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