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

 

Compact weakly symmetric spaces and spherical pairs


Author: H. D. Nguyêñ
Journal: Proc. Amer. Math. Soc. 128 (2000), 3425-3433
MSC (2000): Primary 53C35; Secondary 32M15
Published electronically: May 18, 2000
MathSciNet review: 1676304
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Abstract:

Let $(G,H)$ be a spherical pair and assume that $G$ is a connected compact simple Lie group and $H$ a closed subgroup of $G$. We prove in this paper that the homogeneous manifold $G/H$ is weakly symmetric with respect to $G$ and possibly an additional fixed isometry $\mu$. It follows that M. Krämer's classification list of such spherical pairs also becomes a classification list of compact weakly symmetric spaces. In fact, our proof involves a case-by-case study of the isotropy representations of all spherical pairs on Krämer's list.


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Additional Information

H. D. Nguyêñ
Affiliation: Department of Mathematics, Rowan University, Glassboro, New Jersey 08028
Email: nguyen@rowan.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05425-3
PII: S 0002-9939(00)05425-3
Keywords: Weakly symmetric spaces, spherical pairs, Gelfand pairs
Received by editor(s): April 17, 1998
Received by editor(s) in revised form: January 4, 1999
Published electronically: May 18, 2000
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society