Journal of Lie Theory

no. 3
The Constants of Cowling and Haagerup
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 627-644
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 $\Lambda_G = 21$.
DOI: 10.5802/jolt.516
Classification: 43A30, 22D25, 43A62, 43A90, 43A22
Keywords: Fourier algebra, weak amenability, Gelfand pair, hypergroup 
@article{JOLT_2008_18_3_a9,
     author = {V. Muruganandam},
     title = {The {Constants} of {Cowling} and {Haagerup}},
     journal = {Journal of Lie Theory},
     pages = {627--644},
     year = {2008},
     volume = {18},
     number = {3},
     doi = {10.5802/jolt.516},
     zbl = {1172.43002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.516/}
}
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V. Muruganandam. The Constants of Cowling and Haagerup. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 627-644. doi: 10.5802/jolt.516

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