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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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 $ \mathbf E_n$, where $ n\in\{6,7\}$, 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: http://dx.doi.org/10.1090/S0002-9947-08-04530-3
PII: S 0002-9947(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.