On some developments of the Stokes phenomenon
type: Item
instance of: scholarly article
title: On some developments of the Stokes phenomenon
DOI: 10.1007/978-3-031-30284-8_24
author: Qian Tang
author: Xiaomeng Xu
publication date: 2024-09-17T00:00:00Z
review text: Let \(M\) be the field of the meromorphic in the complex plane functions and \N\[\NY'=AY \tag{1}\N\] \Nbe a linear system of differential equations over \(M\). The key role in the description of the properties of the solutions of system (1) is played by the group differential autorphisms (differential Galois group), which is generated by autorphisms associated with the phenomenon of monodromy (Stokes), in regular (irregular) singular points. However, the calculation of this group is a very difficult task even in the case when system (1) has only two singular points regular and irregular. The paper is a review of several recent publications on this subject (see [\textit{X. Xu}, ``Closure of Stokes matrices. I: Caterpillar points and applications'', Preprint, \url{arXiv:1912.07196}; ``Representations of quantum groups arising from the Stokes phenomenon and applications'', Preprint, \url{arXiv:2012.15673}]).\N\NFor the entire collection see [Zbl 1531.53004].
reviewed by: Mykola Grygorenko
Mathematics Subject Classification ID: 34M40
Mathematics Subject Classification ID: 34M03
Mathematics Subject Classification ID: 34M56
Mathematics Subject Classification ID: 34E20
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 33D80
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 34-02
zbMATH DE Number: 7914668
zbMATH Keywords: Stokes matrix
zbMATH Keywords: isomonodromy deformation
zbMATH Keywords: quantum group
zbMATH Keywords: Gelfand-Tsetlin basis
zbMATH Keywords: crystal basis
zbMATH Keywords: Yangian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7914668