Studies on symmetric functions by algebraic analysis of quantum integrable models
| Project/Area Number |
18K03205
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
Motegi Kohei 東京海洋大学, 学術研究院, 准教授 (30583033)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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)
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| Keywords | 量子可積分系 / 対称関数 / 可解確率過程 / 数え上げ幾何 / 組合せ論 / 楕円対称関数 / Grothendieck多項式 / Grassmann束 / Grothendieck群 / 分配関数 / Whittaker関数 / 楕円パフィアン / 双対公式 / 量子群 / 代数等式 |
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| Outline of Final Research Achievements |
By developing the Izergin-Korepin analysis, we analyzed various partition functions of integrable lattice models and determined their exact forms which are given by factorial versions of symplectic Schur functions, Whittaker functions, elliptic Pfaffians, elliptic multivariable functions. Using the correspondence between partition functions and special functions, we derived identities, dual Cauchy formulas for Whittaker functions, duality between elliptic Pfaffians, for example.
Using Yang-Baxter algebra, we also rederived identities recently discovered and also made application to pushforward formulas in algebraic geometry. We also derived identities and formulas for refined dual Grothendieck polynomials by using partition functions, Yang-Baxter algebra and probability theory.
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| Academic Significance and Societal Importance of the Research Achievements |
対称関数、特殊関数は数理物理、数学における重要な研究対象であり、その性質を可積分系の観点や手法を用いて研究した。可積分系の観点を取り入れることにより、伝統的な手法だけでは捉えられなかったことを捉えることができるようになる。例えば新たな恒等式、公式の導出である。また、関連する代数幾何への応用や、確率論の観点も取り入れて研究することができ、可積分系と数学の他分野との相互作用に貢献できたのではないかと考えている。
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Report
(4 results)
Research Products
(9 results)
