非平稳差分方程与仿射Laumon空间:离散painlevleve方程的量化

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-11-09 DOI:10.3842/sigma.2023.089

Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno, Ryo Ohkawa, Shamil Shakirov, Jun'ichi Shiraishi, Yasuhiko Yamada

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引用次数: 4

摘要

本文给出了作者提出的非平稳差分方程与量子化离散painlevlevev方程的关系。与差分方程相关的五维Seiberg-Witten曲线具有一致的四维极限。我们还证明了原始方程可以被分解为一对函数$\bigl(\mathcal{F}^{(1)}，\mathcal{F}^{(2)}\bigr)$的耦合系统，这是在扩展仿射Weyl群中将哈密顿量识别为平移元素的结果。我们推测，来自仿射Laumon空间的瞬子配分函数为耦合系统提供了一种解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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on-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation

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.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.