Journal of Lie Theory Vol. 12, No. 1, pp. 81112 (2002) 

Mixed Models for Reductive Dual Pairs and Siegel Domains for Hermitian Symmetric SpacesC. S. LeslieC. S. LeslieDepartment of Computer Science Columbia University 1214 Amsterdam Avenue, MC: 0401 New York, NY 100277003, USA cleslie@cs.columbia.edu 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 $G/K$. Full text of the article:
Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
