Small principal series and exceptional duality for two simply laced exceptional groups
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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.References
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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
- MR Author ID: 659045
- Email: hs79@uwindsor.ca
- Received by editor(s): October 10, 2006
- Received by editor(s) in revised form: March 14, 2007
- Published electronically: October 21, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2465824