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

DOI:
https://doi.org/10.1090/S0002-9939-00-05425-3

Published electronically:
May 18, 2000

MathSciNet review:
1676304

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Abstract | References | Similar Articles | Additional Information

Let be a spherical pair and assume that is a connected compact simple Lie group and a closed subgroup of . We prove in this paper that the homogeneous manifold is weakly symmetric with respect to and possibly an additional fixed isometry . 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:
https://doi.org/10.1090/S0002-9939-00-05425-3

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