Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Analytic uniformly bounded representations of $ {\rm SU}(1,n+1)$

Author: Ronald J. Stanke
Journal: Trans. Amer. Math. Soc. 290 (1985), 281-302
MSC: Primary 22E46; Secondary 22E30
MathSciNet review: 787966
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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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Keywords: Fourier analysis on the Heisenberg group, homogeneous norms, spherical principal series, intertwining operators, Laguerre polynomials, gamma function, analytic continuation of operators, uniformly bounded representations
Article copyright: © Copyright 1985 American Mathematical Society