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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation
Hidetoshi Awataa, Koji Hasegawab, Hiroaki Kannoac, Ryo Ohkawade, Shamil Shakirovfg, Jun'ichi Shiraishih, Yasuhiko Yamadai a Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
b Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
c Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan
d Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
e Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University,
Osaka 558-8585, Japan
f University of Geneva, Switzerland
g Institute for Information Transmission Problems, Moscow, Russia
h Graduate School of Mathematical Sciences, University of Tokyo,
Komaba, Tokyo 153-8914, Japan
i Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
Аннотация:
We show the relation of the non-stationary difference equation proposed by one of the authors and the quantized discrete Painlevé VI equation. The five-dimensional Seiberg–Witten curve associated with the difference equation has a consistent four-dimensional limit. We also show that the original equation can be factorized as a coupled system for a pair of functions $\bigl(\mathcal{F}^{(1)}, \mathcal{F}^{(2)}\bigr)$, which is a consequence of the identification of the Hamiltonian as a translation element in the extended affine Weyl group. We conjecture that the instanton partition function coming from the affine Laumon space provides a solution to the coupled system.
Ключевые слова:
affine Laumon space, affine Weyl group, deformed Virasoro algebra, non-stationary difference equation, quantum Painlevé equation.
Поступила: 6 декабря 2022 г.; в окончательном варианте 22 октября 2023 г.; опубликована 9 ноября 2023 г.
Образец цитирования:
Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno, Ryo Ohkawa, Shamil Shakirov, Jun'ichi Shiraishi, Yasuhiko Yamada, “Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation”, SIGMA, 19 (2023), 089, 47 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1984 https://www.mathnet.ru/rus/sigma/v19/p89
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