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 language | English (US) |
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Pages (from-to) | 11-29 |
Number of pages | 19 |
Journal | Selecta Mathematica, New Series |
Volume | 4 |
Issue number | 1 |
DOIs | |
State | Published - 1998 |
Keywords
- Howe duality
- Unipotent representations
ASJC Scopus subject areas
- Mathematics(all)
- Physics and Astronomy(all)