Research on monoids consisting of limits of linear actions on a projective manifold
| Project/Area Number |
15K13421
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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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, 理学研究院, 教授 (70215565)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 代数半群 / 線型代数半群 / コンパクト化 / 超幾何微分方程式系 |
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| Outline of Final Research Achievements |
As a compactification of the projective linear group PGL(V), I have proposed PM(V). It is a compact topological space including PGL(V) as a dense open subset, and it is a monoid acting on the projective space P(V). In addition, I have related it to the well-known compactification -- the wonderful compactification of PGL(V).
In collaboration with Hiroyasu Takeda, I have made a description of the process of confluence of hypergeometric systems a la Gel’fand, as a limit under the adjoint action of a principal nilpotent p-tuple generalizing a principal nilpotent element.
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| Academic Significance and Societal Importance of the Research Achievements |
PGL(V)のコンパクト化として良く知られたワンダフルコンパクト化は，半群ではなく，射影空間P(V)に作用できない。従って，射影空間P(V)に作用できるコンパクトな半群であるPM(V)は学術的意義があり，今後の応用が期待される。
ゲルファント流超幾何微分方程式系は，そのパラメータ空間の双対が，一般線型リー代数の正則元の中心化代数となるものが今まで知られていたが，より一般な主冪零p組の中心化代数となるものを確定特異点型からの変形を含めて考察したことに意義がある。
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Report
(5 results)
Research Products
(4 results)
