| Project/Area Number |
24540002
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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 |
Algebra
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| Research Institution | Hokkaido University |
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Principal Investigator |
SAITO Mutsumi 北海道大学, 理学(系)研究科(研究院), 教授 (70215565)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMASHITA Hiroshi 北海道大学, 大学院理学研究院, 教授 (30192793)
ABE Noriyuki 北海道大学, 大学院理学研究院, 准教授 (00553629)
OKUYAMA Go 北海道科学大学, 保健医療学部, 准教授 (60433421)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | カルタン部分リー代数の変形 / 可換部分リー代数 / グラスマン多様体 / カルタン部分代数の変形 |
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| Outline of Final Research Achievements |
Related to confluence of the systems of hypergeometric equations a la Gelfand, deformation of Cartan subalgebras is studied. Let g be a complex simple Lie algebra of rank n. We have proved that an n-dimensional ideal of a Borel subalgebra is a limit of Jordan Lie subalgebras, which is the centralizer of a regular nilpotent element. Since a Jordan Lie subalgebra is a limit of Cartan subalgebras, an n-dimensional ideal of a Borel subalgebra is also a limit of Cartan subalgebras.
Furthermore, combining with a classical result due to Kostant, we see that the g-module composed of all n-dimensional abelian subalgebras is spanned by Cartan subalgebras or Jordan Lie subalgebras.
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