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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the spectrum of $ (Spin(10,2),SL(2,\mathbb{R}))$ in $ E_{7,3}$


Author: Zhe Du
Journal: Proc. Amer. Math. Soc. 139 (2011), 757-768
MSC (2000): Primary 22E46
Published electronically: September 27, 2010
MathSciNet review: 2736354
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Abstract: We give the complete description of the spectrum of $ (Spin(10,2),SL(2,\mathbb{R}))$ in the minimal representation of $ E_{7,3}$, and we find that it only consists of a discrete spectrum. This is interesting as both groups are noncompact. Also, most of the representations occurring in the spectrum are unitary representations with nonzero cohomology. The representations we obtained have different Hodge types from the representations we obtain from classical theta liftings.


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Additional Information

Zhe Du
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China
Email: duzhe@amss.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10664-0
PII: S 0002-9939(2010)10664-0
Received by editor(s): March 28, 2010
Published electronically: September 27, 2010
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.