2014年3月
CLOSED ORBITS ON PARTIAL FLAG VARIETIES AND DOUBLE FLAG VARIETY OF FINITE TYPE
KYUSHU JOURNAL OF MATHEMATICS
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- ,
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- 巻
- 68
- 号
- 1
- 開始ページ
- 113
- 終了ページ
- 119
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.2206/kyushujm.68.113
- 出版者・発行元
- KYUSHU UNIV, FAC MATHEMATICS
Let G be a connected reductive algebraic group over C. We denote by K = (G(theta))(0) the identity component of the fixed points of an involutive automorphism theta of G. The pair (G, K) is called a symmetric pair. Let Q be a parabolic subgroup of K. We want to find a pair of parabolic subgroups P-1,P- P-2 of G such that (i) P-1 boolean AND P-2 = Q and (ii) P-1 P-2 is dense in G. The main result of this article states that, for a simple group G, we can find such a pair if and only if (G, K) is a Hermitian symmetric pair. The conditions (i) and (ii) imply that the K-orbit through the origin (eP(1), eP(2)) of G/P-1 x G/P-2 is closed and it generates an open dense G-orbit on the product of partial flag variety. From this point of view, we also give a complete classification of closed K-orbits on G/P-1 x G/P-2.
- リンク情報
- ID情報
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- DOI : 10.2206/kyushujm.68.113
- ISSN : 1340-6116
- eISSN : 1883-2032
- CiNii Articles ID : 130004941519
- Web of Science ID : WOS:000341334100005