| Project/Area Number |
21340006
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
NISHIYAMA Kyo 青山学院大学, 理工学部, 教授 (70183085)
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| Co-Investigator(Kenkyū-buntansha) |
WACHI Akihito 北海道教育大学, 教育学部, 准教授 (30337018)
MASUDA Tetsu 青山学院大学, 理工学部, 准教授 (00335457)
KAWAKAMI Hiroshi 青山学院大学, 理工学部, 助教 (00646854)
MATUMOTO Hisayosi 東京大学, 大学院・数理科学研究科, 准教授 (50272597)
YAMASHITA Hiroshi 北海道大学, 大学院・理学研究科, 教授 (30192793)
OCHIAI Hiroyuki 九州大学, マスフォアインダストリ研究所, 教授 (90214163)
谷口 健二 青山学院大学, 理工学部, 准教授 (20306492)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000)
Fiscal Year 2013: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2010: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
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| Keywords | 代数群 / 軌道 / 旗多様体 / 対称空間 / 冪零多様体 / モーメント写像 / 余接束多様体 / 球作用 / 二重旗多様体 / 対称部分群 / ハリシュ・チャンドラ加群 / 随伴サイクル / 余次元1連結性 / 冪零軌道 / Bruhat分解 / KGB理論 / 代数群の軌道 / 随伴多様体 / 多重旗多様体 / 球多様体 / Bruha分解 |
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| Research Abstract |
In mathematics, symmetry is often described by group actions. If the symmetry group is large, the symmetry is considered to be big and "beautiful". One of the most beautiful object in that sense is a homogeneous variety. If the symmetry group is a reductive algebraic group and the homogeneous space is compact, it is called a flag variety. In this research, we studied various orbits on flag varieties using moment maps.
Main results are the followings. (i) We constructed many double flag varieties of finite type, and in good cases, we succeeded in classification of such varieties. (ii) For an irreducible unitary representation of a real reductive group, one can consider an associated variety. We defined codimension one connectedness among nilpotent orbits, and constructed irreducible representations whose assocaited varieties are maximally connected in cosimension one.
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