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Compact weakly symmetric spaces and spherical pairs
Author(s):
H.
D.
Nguyêñ
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3425-3433.
MSC (2000):
Primary 53C35;
Secondary 32M15
Posted:
May 18, 2000
MathSciNet review:
1676304
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Abstract:
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:
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
Posted:
May 18, 2000
Communicated by:
Roe Goodman
Copyright of article:
Copyright
2000,
American Mathematical Society
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