Tensor products of singular representations and an extension of the
$ \theta $-correspondence |
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Authors: | A Dvorsky S Sahi |
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Institution: | (1) Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, e-mail: dvorsky@math.rutgers.edu, e-mail: sahi@math.rutgers.edu, US |
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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 . Our procedure establishes a correspondence between certain unitary representations of G and those of . This extends the usual -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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Keywords: | , Unipotent representations, Howe duality, |
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