Combinatorics of special polynomials associated to certain solutions of Painleve equations
Project/Area Number |
15K13425
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Nagoya University |
Principal Investigator |
Okada Soichi 名古屋大学, 多元数理科学研究科, 教授 (20224016)
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | Painleve 方程式 / KP 階層 / 対称関数 / Schur 関数 / Schur Q 関数 / 組合せ論 / Painleve方程式 |
Outline of Final Research Achievements |
We study several aspects of integrable systems and symmetric functions, toward unraveling combinatorial structure of special polynomials associated to certain solutions of the Painleve-type equations. 1. We find Giambelli-type determinant identities, which characterize the expansion coefficients of the \tau-function of the KP hierarchy, and give new determinant expressions for Schur functions. 2. We find a relation between two generalizations of Schur Q-functions corresponding to rational Schur functions. Also we give several identities and positivity conjectures for Schur Q-functions associated to the root system of type C.
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Report
(4 results)
Research Products
(13 results)