Tensor products of singular representations and an extension of the theta-correspondence

Alexander Dvorsky; Siddhartha Sahi

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arXiv · math/9805002

Tensor products of singular representations and an extension of the theta-correspondence

Alexander Dvorsky·Siddhartha Sahi

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Abstract

In this paper we consider the problem of decomposing tensor products of certain singular unitary representations of a semisimple Lie group G. Using explicit models for these representations (constructed earlier by one of us) we show that the decomposition is controlled by a reductive homogeneous space G'/H'. Our procedure establishes a correspondence between certain unitary representations of G and those of G'. This extends the usual theta--correspondence for dual reductive pairs. As a special case we obtain a correspondence between certain representations of real forms of E_7 and F_4.

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BibTeX RIS

Alexander Dvorsky, Siddhartha Sahi. 1998-05-01. Tensor products of singular representations and an extension of the theta-correspondence. https://arxiv.org/abs/math/9805002

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