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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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | Painleve / Poschl-Teller models / Umemura polynomials / Combinatorics / Painleve equations / Hessenberg varies / Fomin-Kirillov algebras / FK algebras / Classical Schubert / Quantum Schubert / Grothendieck Calculi / Classical RSK / Tropical RSK / Probabilistic models / Integrable Systems / FK-algebras / Cohomology theories / Flag varieties / Integrable systems / Quadratic algebras / Quantum K-theory / Painleve & Bethe Ansatz / Quantum cohomology / Elliptic Functions / 代数学 / 代数的組み合わせ論 |
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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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| 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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Report
(7 results)
Research Products
(76 results)
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[Presentation] On some quadratic algebras2016
Author(s)
A.N.Kirillov
Organizer
Lecture course "On some quadratic algebras"
Place of Presentation
The Stockholm University, Sweden
Year and Date
2016-10-13
Related Report
Int'l Joint Research / Invited
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[Book] ベーテ仮設の数理2021
Author(s)
坂本玲峰, アナトール N. キリロフ
Total Pages
320
Publisher
森北出版
ISBN
9784627082410
Related Report
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