Compact weakly symmetric spaces and spherical pairs

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 μ. 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.

Original languageEnglish (US)
Pages (from-to)3425-3433
Number of pages9
JournalProceedings of the American Mathematical Society
Volume128
Issue number11
StatePublished - Dec 1 2000

Fingerprint

Symmetric Spaces
Lie groups
Homogeneous Manifold
Isotropy
Simple group
Isometry
Subgroup
Closed

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

@article{3dcb0bcb5cad40fe8cfc6aa5542cb726,
title = "Compact weakly symmetric spaces and spherical pairs",
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 μ. It follows that M. Kr{\"a}mer'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 Kr{\"a}mer's list.",
author = "Hieu Nguyen",
year = "2000",
month = "12",
day = "1",
language = "English (US)",
volume = "128",
pages = "3425--3433",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "11",

}

Compact weakly symmetric spaces and spherical pairs. / Nguyen, Hieu.

In: Proceedings of the American Mathematical Society, Vol. 128, No. 11, 01.12.2000, p. 3425-3433.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Compact weakly symmetric spaces and spherical pairs

AU - Nguyen, Hieu

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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 μ. 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.

AB - 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 μ. 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.

UR - http://www.scopus.com/inward/record.url?scp=24844457335&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24844457335&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:24844457335

VL - 128

SP - 3425

EP - 3433

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -