In this paper we study spherical unitary highest weight representations associated to a compactly causal symmetric space and use the results to prove estimates for the corresponding spherical functions of the c-dual non-compactly causal symmetric space. Such estimates turn out to be useful in determ
Symmetric spaces and star representations: II. Causal symmetric spaces
β Scribed by P. Bieliavsky; M. Pevzner
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 96 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0393-0440
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β¦ Synopsis
We construct and identify star representations canonically associated with holonomy-reducible simple symplectic symmetric spaces. This leads a non-commutative geometric realization of the correspondence between causal symmetric spaces of Cayley-type and Hermitian symmetric spaces of tube-type.
π SIMILAR VOLUMES
In this paper we study representations of the automorphism groups of classical infinite-dimensional tube domains. In particular we construct the L 2 -realization of all unitary highest weight representations, including the vector-valued case. We also find a projective representation of the full iden
In [Z] we have introduced and studied generalized symmetric RIEafA"ian spaces. In the present paper we introduce the concept of a generalized affine symmetric space. We also define the group of transvections of such a space, m d we give s ~m e basic properties of this group. Following 0. LOOS, a sy
We determine integral formulas for the meromorphic extension in the \*-parameter of the spherical functions . \* on a noncompactly causal symmetric space. The main tool is Bernstein's theorem on the meromorphic extension of complex powers of polynomials. The regularity properties of . \* are deduced