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

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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.
19 pages, to appear in Selecta Math 4(1998)

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Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/76885

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9805002
 http://arxiv.org/abs/math/9805002

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arXiv