Research on the geometric representation theory using algebraic analysis
| Project/Area Number |
15K04790
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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 | Osaka City University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
兼田 正治 大阪市立大学, 大学院理学研究科, 教授 (60204575)
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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: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 代数解析 / 代数群 / 量子群 / 表現 |
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| Outline of Final Research Achievements |
I obtained several results concerning the representation theory of quantum groups at roots of 1. The most important aim was to establish the Beilinson-Bernstein type correspondence for quantum groups at roots of 1. The problem is not yet solved in its full generality, but I have established it for the quantum groups of type A. This is a big progress. In connection with the quantum groups at even roots of 1, I also considered the quantum groups at q=-1 and proved that it is isomorphic to the enveloping algebra of a Lie multi-super algebra. I investigated also the quantized coordinate algebras and affine Hecke algebras, but obtained no remarkable results on them.
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Report
(4 results)
Research Products
(10 results)
