Small principal series and exceptional duality for two simply laced exceptional groups

Author:
Hadi Salmasian

Journal:
Trans. Amer. Math. Soc. **361** (2009), 1925-1947

MSC (2000):
Primary 22E46, 22E50, 11F27

DOI:
https://doi.org/10.1090/S0002-9947-08-04530-3

Published electronically:
October 21, 2008

MathSciNet review:
2465824

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Abstract: We use the notion of rank defined in an earlier paper (2007) to introduce and study two correspondences between small irreducible unitary representations of the split real simple Lie groups of types , where , and two reductive classical groups. We show that these correspondences classify all of the unitary representations of rank two (in the sense of our earlier paper) of these exceptional groups. We study our correspondences for a specific family of degenerate principal series representations in detail.

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Additional Information

**Hadi Salmasian**

Affiliation:
Department of Mathematics and Statistics, University of Windsor, Lambton Tower, 10th Floor, Windsor, Ontario, Canada N9B 3P4

Email:
hs79@uwindsor.ca

DOI:
https://doi.org/10.1090/S0002-9947-08-04530-3

Keywords:
Kirillov's orbit method,
Mackey analysis,
theta correspondence,
unitary representations

Received by editor(s):
October 10, 2006

Received by editor(s) in revised form:
March 14, 2007

Published electronically:
October 21, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.