### 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 language | English (US) |
---|---|

Pages (from-to) | 3425-3433 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 11 |

State | Published - Dec 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*128*(11), 3425-3433.

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*Proceedings of the American Mathematical Society*, vol. 128, no. 11, pp. 3425-3433.

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

Research output: Contribution to journal › Article

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 -