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
Full-text PDF
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