2000 Fiscal Year Final Research Report Summary
Algebraic analysis of representation theory
| Project/Area Number |
09304003
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| Research Category |
Grant-in-Aid for Scientific Research (A).
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | KYOTO UNIVERSITY, RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES |
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Principal Investigator |
KASHIWARA Masaki Kyoto University, Research Institute for Mathematical Sciences, P., 数理解析研究所, 教授 (60027381)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIYAMA Kyo Kyoto University, Faculty of Integrated Human Studies, A.P., 総合人間学部, 助教授 (70183085)
GYOJA Akihiko Graduate School of Mathematics, Nagoya University, P., 大学院・多元数理科学研究科, 教授 (50116026)
MIWA Tetsuji Kyoto University, Department of Mathematics, P., 大学院・理学研究科, 教授 (10027386)
OKADA Soichi Nagoya University, Faculty of Integrated Arts and Sciences, A.P., 大学院・多元数理科学研究科, 助教授 (20224016)
KUROKI Gen Graduate School of Sciences and Faculty, Tohoku University, A., 大学院・理学研究科, 助手 (10234593)
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| Project Period (FY) |
1997 – 2000
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| Keywords | representation theory / quantum groups / solvable models / combinatorics |
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| Research Abstract |
With this grant, we have studied the representations of Lie groups, quantum algebras, Hecke algebras, etc. in the point of view of mathematical Physics and Combinatorics.
In the first year (19997), the activities are closely tied with RIMS project 1997 (Representation theory). In this project, we focused our activity on the study of the representations of real Lie groups from the geometrical view point of homogeneous spaces. With around 40 participants from abroad, the international science exchange was performed successfully. These results are published in Advanced Studies in Pure Mathematics, vol.26.
In 1998, the activities are closely tied with RIMS project 1998 (Combinatorial methods in representation theory). We had around 25 participants from abroad. Main theme was the representation of quantum groups and affine Hecke algebras.
In 1999, we focused on mathematical physics, and held the international symposium "Physical Combina-torics" at International Institute for advanced study and Research Institute for mathematical Sciences. We had advances in the representation theory of quantum algebras, the structure of solutions to Kniznik-Zamolodhikov equations and its q-analogy, conformal field theory. These activities were published in "Physical Combinatorics, Progress in Math. vol.191, Birkhauser.
In the last year 2000, we organized the international symposium "Math-Odyssey2001" in order to summarize our four years activities. The main theme was algebro-analytic methods in representation theory and mathematical physics. The proceedings will be published by the publisher Birkhauser.
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