Extension and application of antipodal sets in symmetric spaces
| Project/Area Number |
15K04835
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TANAKA MAKIKO 東京理科大学, 理工学部, 教授 (20255623)
IKAWA OSAMU 京都工芸繊維大学, 工芸科学研究科, 教授 (60249745)
IRIYEH HIROSHI 茨城大学, 理学部, 准教授 (30385489)
AKAI TAKASHI 首都大学東京, 理工学研究科, 准教授 (30381445)
OKUDA TAKAYUKI 広島大学, 理学研究科, 講師 (40725131)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 対称空間 / 対蹠集合 / 実形の交叉 / 複素旗多様体 / 有向実Grassmann多様体 / 対称三対 / 実旗多様体 / スピノル群 |
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| Outline of Final Research Achievements |
We classified maximal antipodal subgroups in the quotient groups of classical compact Lie groups. By the use of these results we also classified maximal antipodal subgroups in the automorphism groups of classical compact Lie algebras. We showed that the discrete intersection of two real forms in a complex flag manifold is an antipodal set and using this we determined the Lagrangian Floer homology for two real forms. This is a generalization of our previous results on the intersections of real forms in Hermitian symmetric spaces of compact type. We associated maximal antipodal sets in real oriented Grassmann manifolds with certain combinatorial objects. Using this we estimated the cardinalities of antipodal sets of rank 5 and constructed some sequences of maximal antipodal sets of general rank. We found some fundamental sequences with which we can reconstruct maximal antipodal sets we have already found.
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Report
(4 results)
Research Products
(51 results)
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[Presentation] 実形の交叉2017
Author(s)
田崎博之
Organizer
第２４回沼津研究会
Place of Presentation
沼津工業高等専門学校(静岡県沼津市)
Year and Date
2017-03-06
Related Report
Invited
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[Presentation] 対蹠集合と実形の交叉2016
Author(s)
田崎博之
Organizer
第11回代数・解析・幾何学セミナー
Place of Presentation
鹿児島大学理学部(鹿児島県鹿児島市)
Year and Date
2016-02-16
Related Report
Invited
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[Presentation] 対称空間の対蹠集合2015
Author(s)
田崎博之
Organizer
第62回幾何学シンポジウム
Place of Presentation
東京理科大学神楽坂キャンパス(東京都新宿区)
Year and Date
2015-08-30
Related Report
Invited
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