2023 Fiscal Year Final Research Report
Multiple hypergeometric series, screening operators and elliptic integrable systems associated with affine root systems
Project/Area Number |
19K03512
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 12010:Basic analysis-related
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Research Institution | The University of Tokyo |
Principal Investigator |
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Project Period (FY) |
2019-04-01 – 2024-03-31
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Keywords | affine Laumon space / Ruijsenaars system / affine screenings / q-Painleve VI equation / Shakirov equation / q-KZ equation |
Outline of Final Research Achievements |
We obtained several conjectures (duality conjectures, conjecture of non-stationary Ruijsenaars equation, conjecture for degeneration to the elliptic Ruijsenaars functions) concerning the non-stationary Ruijsenaars functions. We establish the relation between the non-stationary difference equation proposed by S. Shakirov and the quantized discrete Painleve VI equation due to K. Hasegawa (quantization of Jimbo-Sakai's equation). We show that Shakirov’s non-stationary difference equation, when it is truncated, implies the quantum Knizhnik-Zamolodchikov (q-KZ) equation with generic spins. We prove that the affine Laumon partition function gives a solution to Shakirov’s equation.
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Free Research Field |
量子代数の表現論と量子可積分系
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Academic Significance and Societal Importance of the Research Achievements |
楕円Ruijsenaars系の非定常方程類似と考えられる系に関する(実験的)研究を, affine Laumon空間の上の幾何学を用いて行なった. affine screening 作用素を用いて非定常Ruijsenaars関数を表現する可能性について, 一連の予想を得た. また, 非定常方程式はパンルベ方程式をその代表として含む重要な研究対象でもある. 本研究では, 量子q差分系における非定常方程式を発見し, その固有関数の明示的公式の持つ組合わせ的構造に関する研究を行なった. 今後も, affine Laumon空間の幾何学を軸として, さまざまな発見がもたらされると期待される.
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