2017 Fiscal Year Final Research Report
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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| 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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| Free Research Field |
代数群と量子群の表現論
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