Analytic uniformly bounded representations of 𝑆𝑈(1,𝑛+1)

Stanke, Ronald J.

doi:10.1090/S0002-9947-1985-0787966-1

Analytic uniformly bounded representations of $\textrm {SU}(1,n+1)$
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by Ronald J. Stanke PDF

Trans. Amer. Math. Soc. 290 (1985), 281-302 Request permission

Abstract:

By analytically continuing suitably normalized spherical principal series, a family of uniformly bounded representations of $SU(1,n + 1)$, all of which act on the same Hilbert space ${L^2}({{\mathbf {R}}^{2n + 1}})$, is constructed which is parametrized by complex numbers $s$ lying in the strip $- 1 < \operatorname {Re} (s) < 1$. The proper normalization of the principal series representations involves the intertwining operators of equivalent principal series representations. These intertwining operators are first analyzed using Fourier analysis on the Heisenberg group.

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