A Lax Formulation of a Generalized q-Garnier System

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2021-11-27 DOI:10.1007/s11040-021-09412-3

Takao Suzuki

引用次数: 3

Abstract

Recently, a birational representation of an extended affine Weyl group of type \(A_{mn-1}^{(1)}\times A_{m-1}^{(1)}\times A_{m-1}^{(1)}\) was proposed with the aid of a cluster mutation. In this article we formulate this representation in a framework of a system of q-difference equations with \(mn\times mn\) matrices. This formulation is called a Lax form and is used to derive a generalization of the q-Garnier system.

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广义q-Garnier系统的一个松弛公式

最近，一个扩展仿射Weyl群\(A_{mn-1}^{(1)}\times A_{m-1}^{(1)}\times A_{m-1}^{(1)}\)型的一种双族表示被提出与一个簇突变的援助。在这篇文章中，我们在一个含有\(mn\times mn\)矩阵的q-差分方程组的框架中表述了这个表示。这个公式称为Lax形式，并用于推导q-Garnier系统的推广。

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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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.