2021 Fiscal Year Final Research Report
Combinatorics around Painleve VI
| Project/Area Number |
16K05057
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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 | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2022-03-31
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| Keywords | Painleve / Poschl-Teller models / Umemura polynomials / Combinatorics |
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| Outline of Final Research Achievements |
Proof of old standing Conjecture that the all coefficients of the two parameter Umemura polynomials are integer numbers and gave their explicit formulas (partly joint with M.Taneda and P. van Diejen). Some quantum and elliptic generalizations are suggested.
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| Free Research Field |
Integrabl Systems, Combinatorics
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| Academic Significance and Societal Importance of the Research Achievements |
Our results explained and proved Conjecture that coefficients of Umemura polynomials are integers , and pointed out on surprising connections of Painleve and Poschl-Teller models and Combinatorics and Representation Theory.
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