Can I read Canonical Representations Related to Hyperbolic Spaces on EtoBox?

Canonical Representations Related to Hyperbolic Spaces by G. van Dijk; S.C. Hille is a Mathematics article available to read on EtoBox.

What is Canonical Representations Related to Hyperbolic Spaces about?

We extend the notion of canonical representation, introduced by A. M. Vershik, I. M. Gel'fand and M. I. Graev (1982, in ``Representation Theory,'' Cambridge Univ. Press, Cambridge, U.K.), to all (classical) rank one semisimple Lie groups. We determine the spectral decomposition of the canonical representations in detail. ## 1997 Academic Press In [15] Vershik, Gel'fand and Graev introduced the very interesting class of so-called canonical representations ? \* of SU(1, 1). These are unitary representations, realized on X=SU(1, 1)ÂU(1), which, when suitably scaled, asymptotically tend to the left regular representation of SU(1, 1) on X if \* Ä . Their spectral decomposition has also been determined by the above authors. The notion of canonical representation can naturally be extended to Hermitian symmetric spaces (see [14]) and thus fits into the famous work of Berezin on quantization and also into the theory of the analytic continuation of the holomorphic discrete series (cf. [2, 13, 16]). In this note we extend it to the classical hyperbolic spaces over F=R, C and H. We determine the asymptotic behaviour if \* Ä by a direct method, and the spectral decomposition. Our method is diff

Who reads Canonical Representations Related to Hyperbolic Spaces?

Author

G. van Dijk; S.C. Hille

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

1997

Language

EN

Field

Mathematics (Physical Sciences)