2016 Fiscal Year Final Research Report
Algebraic combinatorics of plane partitions and alternating sign matrices, and related representation theory and mathematical physics
Project/Area Number |
24340003
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Research Category |
Grant-in-Aid for Scientific Research (B)
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Allocation Type | Partial Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Nagoya University |
Principal Investigator |
Soichi Okada 名古屋大学, 多元数理科学研究科, 教授 (20224016)
|
Co-Investigator(Kenkyū-buntansha) |
石川 雅雄 琉球大学, 教育学部, 教授 (40243373)
松本 詔 鹿児島大学, 理学部, 准教授 (60547553)
中西 知樹 名古屋大学, 多元数理科学研究科, 教授 (80227842)
|
Project Period (FY) |
2012-04-01 – 2017-03-31
|
Keywords | 平面分割 / 交代符号行列 / 対称関数 / Pfaffian / KP 階層 / 複素鏡映群 |
Outline of Final Research Achievements |
We study various aspects of algebraic combinatorics related to plane partitions and alternating sign matrices. 1. We establish Pfaffian analogues of the Cauchy-Binet formula and prove several identities among Schur Q-functions and their generalizations. 2. We prove the generating function for Young books can be written as a q-Selberg-type integral. 3. By establishing Pieri rules for classical groups, we give another proof to Burrill's conjecture and find its generalizations. 4. We find Giambelli-type determinant identities for the expansion coefficients of the \tau-function of the KP hierarchy, and prove that these determinant identities characterize solutions of the KP hierarchy.
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Free Research Field |
組合せ論,表現論
|