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

Alexander Dvorsky, Siddhartha Sahi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 θ-correspondence for dual reductive pairs. As a special case we obtain a correspondence between certain representations of real forms of E7 and F4.

Original languageEnglish (US)
Pages (from-to)11-29
Number of pages19
JournalSelecta Mathematica, New Series
Volume4
Issue number1
DOIs
StatePublished - 1998
Externally publishedYes

Keywords

  • Howe duality
  • Unipotent representations

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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