2001 Fiscal Year Final Research Report Summary
Study of special functions based on representation and invariant theories
| Project/Area Number |
11440043
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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 |
Basic analysis
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
UMEDA Toru Math. Dept., Kyoto University, Associte Professor, 大学院・理学研究科, 助教授 (00176728)
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| Co-Investigator(Kenkyū-buntansha) |
NOUMI Masatoshi Math. Dept., Kobe Univ., Prof., 大学院・自然科学研究科, 教授 (80164672)
MATSUZAWA Junichi Dept. of technology, Kyoto University, Lecturer, 大学院・工学研究科, 講師 (00212217)
NOMURA Takaaki Math. Dept., Kyoto University, Assoc. Prof., 大学院・理学研究科, 助教授 (30135511)
OEHIAI Hiroyuki Math. Dept. Tokyo Inst. Technology, Assoc. Prof., 大学院・理学研究科, 助教授 (90214163)
WAKAYAMA Masato Graduate School of Math. Kyushu Univ., Prof., 大学院・数理学研究院, 教授 (40201149)
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| Project Period (FY) |
1999 – 2001
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| Keywords | special functions / representation theory / invariant theory / invariant differential operations / Copelli identity / hypergeometric functions / determinant / Pfaphan |
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| Research Abstract |
The main object of the research is to find the group theoretical background behind the world of special functions and to utilize the symonetious for the special functions. Among them the theory of "dual pairs" is the key to our study, which explains many phenomina from the view-point of representation theory and the theory of invariants. We have Capilli type identities, now commtative harnomic oscillatws as the typical investizations where and pains work very well as the griding principle. On the other hand, for the hyprogeinctic from Rons and Pain lene transcendents, we have claified the grop gymmetric behind them. The helps a lot for deeper investigations of these fnctions.
As for the Capelli type identities, we got many interesting formlas including permanets and Pfuffians, not only for the determinants, Furthermore we found some Capelli type identity corresponding to the "group determinant". The invariant theoretic backgroud conneits these identities to some sphenicel functions. There are sort of unification of various objects.
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