| Project/Area Number |
09440020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyushu University |
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Principal Investigator |
MIMACHI Katsuhisa Kyushu University, Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (40211594)
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Yasuhiko Kobe University, Graduate School of Science and Technology, Associate Professor, 大学院・自然科学研究科, 助教授 (00202383)
NOUMI Masatoshi Kobe University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (80164672)
HANAMURA Masaki Kyushu University, Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (60189587)
渡辺 文彦 九州大学, 大学院・数理学研究科, 助手 (20274433)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥9,800,000 (Direct Cost: ¥9,800,000)
Fiscal Year 1999: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1997: ¥3,800,000 (Direct Cost: ¥3,800,000)
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| Keywords | hypergeometric functions / integrals / representation theory / Macdonald polynomials / QKZ equation / Selberg integrals / de Rham theory / Painleve equation / de Rham理論 / q-差分系 / Hecke環 / セルバーグ型積分 |
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| Research Abstract |
The purpose of the present research was to settle the viewpoint to unify the theory of hypergeometic function associated with the root system and the theory of integrals. Concrete theme of this work was the following : 1. De Rham theory (Study of homology and cohomology associated with Selberg type integrals, which appear as the spherical functions of A type), 2. Relationship between the representations of several kinds of algebras (Hecke algebras and so on) and the integrals, 3. Application to Painleve equations (special polynomials such as Okamoto polynomials), 4. Application to mathematical physics (Calogero system, correlation functions in conformal field theory or solvable lattice models). The results of the head investigator were mainly about 1 and 2, those of Hanamura were about 2, those of Noumi and Yamada were about 3. Matsui's help was valuable in the study of 4, Ochiai's in 2 and 4, Wakayama's in 2, Kato's in 1.
Anyway, we have obtained a lot of results through the period of the present research project. As an evidence, many of papers had appeared in the journal of excellent level.
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