亲和韦尔群与非阿贝尔离散系统：对 $d$-Painlevé 方程的应用

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-03-27 DOI:arxiv-2403.18463

Irina Bobrova

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引用次数: 0

摘要

本文介绍了仿射韦尔群双向表示的非阿贝尔广义化及其在离散动力系统中的应用。通过使用这种广义化，推导出了$A_n^{(1)}$, $n \geq 2$ 类型的离散系统和带有附加动力的$d$-Painlev\'e方程的非交换类比。此外，还讨论了后者的凝聚级联。

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Affine Weyl groups and non-Abelian discrete systems: an application to the $d$-Painlevé equations

A non-abelian generalisation of a birational representation of affine Weyl groups and their application to the discrete dynamical systems is presented. By using this generalisation, non-commutative analogs for the discrete systems of $A_n^{(1)}$, $n \geq 2$ type and of $d$-Painlev\'e equations with an additive dynamic were derived. A coalescence cascade of the later is also discussed.

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arXiv - PHYS - Exactly Solvable and Integrable Systems

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