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	Tensor products of holomorphic representations and bilinear differential operators
	Peng, LH ; Zhang, GK
	2004
关键词	weighted Bergman spaces reproducing kernel spaces tensor products bounded symmetric domains bilinear differential operators representations of Lie groups homogeneous tuples of operators BOUNDED SYMMETRIC DOMAINS REPRODUCING KERNELS DISCRETE-SERIES SPACES FORMS
英文摘要	Let H-v be the weighted Bergman space on a bounded symmetric domain D = G/K. It has analytic continuation in the weight v and for v in the so-called Wallach set H-v still forms unitary irreducible (projective) representations of G. We give the irreducible decomposition of the tensor product H-v1 circle times H-v2 of the representations for any two unitary weights v and we find the highest weight vectors of the irreducible components. We find also certain bilinear differential intertwining operators realizing the decomposition, and they generalize the classical transvectants in invariant theory of SL(2, C). As applications, we find a generalization of the Bol's lemma and we characterize the multiplication operators by the coordinate functions on the quotient space of the tensor product H-v1 circle times H-v2 modulo the subspace of functions vanishing of certain degree on the diagonal. (C) 2003 Elsevier Inc. All rights reserved.; Mathematics; SCI(E); 0; ARTICLE; 1; 171-192; 210
语种	英语
出处	SCI
出版者	journal of functional analysis
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/255065]
专题	数学科学学院
推荐引用方式 GB/T 7714	Peng, LH,Zhang, GK. Tensor products of holomorphic representations and bilinear differential operators. 2004-01-01.

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