EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 12, No. 1, pp. 81--112 (2002)

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Mixed Models for Reductive Dual Pairs and Siegel Domains for Hermitian Symmetric Spaces

C. S. Leslie

C. S. Leslie
Department of Computer Science
Columbia University
1214 Amsterdam Avenue, MC: 0401
New York, NY 10027-7003, USA

Abstract: Let $(G,G^\prime)$ be the reductive dual pair $(Sp(n,\Bbb R),O(k))$ or $(U(p,q),U(k))$, and let $K$ be a maximal compact subgroup of the noncompact group $G$. Then for the representations $\pi$ of $\widetilde{G}$ which occur in the Howe duality correspondence for $(G,G^\prime)$, we construct explicit intertwining maps between mixed models of $\pi$ and spaces of holomorphic sections of vector bundles over the hermitian symmetric space $G/K$, where $G/K$ is embedded in its holomorphic tangent space as a type III Siegel domain. This result provides a link between the original construction of these representations using tube domain and type II Siegel domain realizations of $G/K$ and more recent constructions using the bounded domain realization of $G/K$.

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Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.

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