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Representations in L2-Spaces on Infinite-Dimensional Symmetric Cones

✍ Scribed by Karl-Hermann Neeb; Bent Ørsted

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
311 KB
Volume
190
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 identity component of the affine automorphism group of the Hilbert-Schmidt version of the tube domain with trivial cocycle on the subgroup corresponding to the trace class version, but non-trivial on the large group. Finally we show that the operator-valued measures corresponding to the vector valued highest weight representations have densities of a rather weak type with respect to Wishart distributions which makes it possible to determine their ''supports.''

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