1992 Fiscal Year Final Research Report Summary
Study of Mathematical Sciences by Algebraic Methods
| Project/Area Number |
03302001
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
HOTTA Ryoshi Tohoku U.Fac.Sci.,Professor, 理学部, 教授 (70028190)
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| Co-Investigator(Kenkyū-buntansha) |
TANISAKI Toshiyuki Hiroshima U.Fac.Sci.,Professor, 理学部, 教授 (70142916)
KAWANAKA Noriaki Osaka U.Fac.Sci.,Professor, 理学部, 教授 (10028219)
MIWA Tetsuji Kyoto U.RIMS,Professor, 数理解析研, 教授 (10027386)
MORITA Yasuo Tohoku U.Fac.Sci.,Professor, 理学部, 教授 (20011653)
ODA Tadao Tohoku U.Fac.Sci.,Professor, 理学部, 教授 (60022555)
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| Project Period (FY) |
1991 – 1992
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| Keywords | Invariant Theory / Duality / Quantum Groups / Algebraic Groups / Moduli of Vector Bundles / Hypergeometric Differential Equations / Conformal Fields / Number Theory |
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| Research Abstract |
The following conferences are organized and/or supported according to the main point of this project: 1.Symposium of Algebraic Geometry(1991.10.1-4,Kyoto Univ.) 2.New Trend of Invariant Theory(1991.12.16-18,Osaka Univ.) 3.Duality as Phenomenon(1992.8.4-6,Hakodate) 4.Quantum Groups and Related Topics(1992.10.3-5,Nagoya Univ.) 5.Representations of Algebraic Groups(1992.10.29-31,Tohoku Univ.)
The details are in the separated booklet "Report of the Results of the Project" and here is only a summary.
In Conf.1, the structure of moduli of vector bundles, which is also interested in mathematical physics, was a main topic and many related results were reported.
Conf.2 was organized by the head investigator and some of the others. There we tried to investigate the role of invariant theory, one of the main themes of classical algebra, in the modern analysis including mathematical physics. Varieties of topics were hypergeometric differential equations, representations of quantum groups, and conformal field theory.
Conf.3 is rather an unusual meeting where distinguished mathematicians of quite varieties of fields attended and discussed the concept "Duality" in mathematics (and even outer world). Many problems and results were proposed from number theory to physics. The proceedings will be soon published by the organizers.
For Conf.4, we supported the publication of its proceedings.
Conf.5 is for discussions of recent results and problems in somewhat traditional representation theory. Together with three foreign experts as participants,many results were reported including their technical points.
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