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

A. Dvorsky ^[1] ; S. Sahi ^[1]
1. [1] Rutgers University
  
  Rutgers University
  
  City of New Brunswick, Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 4, Nº. 1, 1998, págs. 11-29
Idioma: inglés
DOI: 10.1007/s000290050023
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Resumen
- 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 θ -correspondence for dual reductive pairs. As a special case we obtain a correspondence between certain representations of real forms of E7 and F4.