CLOSED ORBITS ON PARTIAL FLAG VARIETIES AND DOUBLE FLAG VARIETY OF FINITE TYPE
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- KONDO Kensuke
- Department of Physics and Mathematics Aoyama Gakuin University
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- NISHIYAMA Kyo
- Department of Physics and Mathematics Aoyama Gakuin University
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- OCHIAI Hiroyuki
- Institute of Mathematics-for-Industry Kyushu University
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- TANIGUCHI Kenji
- Department of Physics and Mathematics Aoyama Gakuin University
Description
Let G be a connected reductive algebraic group over C. We denote by K = (Gθ)0 the identity component of the fixed points of an involutive automorphism θ 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 P1, P2 of G such that (i) P1 ∩ P2 = Q and (ii) P1 P2 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 (eP1, eP2) of G/P1 × G/P2 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/P1 × G/P2.
Journal
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- Kyushu Journal of Mathematics
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Kyushu Journal of Mathematics 68 (1), 113-119, 2014
Faculty of Mathematics, Kyushu University
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Details 詳細情報について
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- CRID
- 1390282680204507136
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- NII Article ID
- 130004941519
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- ISSN
- 18832032
- 13406116
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed