The constants of Cowling and Haagerup. (English) Zbl 1172.43002
Summary: We give a simpler proof of the main theorem of M. Cowling and U. Haagerup [Invent. Math. 96, 507–549 (1989; Zbl 0681.43012)], 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 \(\Lambda_G = 21\).
MSC:
| 43A30 | Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. |
| 22D25 | \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations |
| 43A62 | Harmonic analysis on hypergroups |
| 43A90 | Harmonic analysis and spherical functions |
| 43A22 | Homomorphisms and multipliers of function spaces on groups, semigroups, etc. |
