Combinatorics of special polynomials associated to certain solutions of Painleve equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13425
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• 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
• Keywords: Painleve 方程式 / KP 階層 / 対称関数 / Schur 関数 / Schur Q 関数

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.

Free Research Field

組合せ論，表現論