Electronic Resource
Springer
Transformation groups
5 (2000), S. 325-350
ISSN:
1531-586X
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract IfS=G Exp (iW) is a complex open Ol'shanskiî semigroup, whereW is an open elliptic cone, then we considerG-biinvariant domainsD=G Exp (iD g)S. First we show that the representation ofG×G on eachG-biinvariant irreducible reproducing kernel Hilbert space in Hol(D) is a highest weight representation whose kernel is the character of a highest weight representation ofG. In the second part of the paper we explain how to construct biinvariant Kähler structures on biinvariant Stein domains and show by a certain Legendre transform that the so obtained symplectic manifolds are isomorphic to domains in the cotangent bundleT * (G).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01234796
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