Research on the representation theory of algebraic groups using algebraic analysis
| Project/Area Number |
24540026
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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) |
KANEDA Masaharu 大阪市立大学, 大学院理学研究科, 教授 (60204557)
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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| Co-Investigator(Renkei-kenkyūsha) |
SAITO Yoshihisa 東京大学, 大学院数理科学研究科, 准教授 (20294522)
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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: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 代数解析 / 代数群 / 表現 / 量子群 / 表現論 / 国際研究者交流(アメリカ) |
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| Outline of Final Research Achievements |
We completely determined the structure of the center of a quantized enveloping algebra at an odd root of unity. This gives the variety consisting of central characters. In order to develop the representation theory we need more information about the Poisson structure of this variety. We have almost accomplished it although there remain some points to be checked. We also investigated the representation theory of quantized coordinate algebras. In particular, we have given a description of the Soibelman module via generators and relations. Using this we gave a unified proof of a result of Kuniba-Okado-Yamada. Moreover, we gave a proof of their conjecture. We investigated the Drinfeld pairing of the quantized enveloping algebra by algebraic methods. We gave a new simpler proof of the fact that the Drinfeld pairing is invariant under the action of the braid group.
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Report
(4 results)
Research Products
(10 results)
