Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'487'895
Articles rated: 2609

29 March 2024
 
  » arxiv » 1912.7196

 Article overview


Closure of Stokes matrices I: caterpillar points and Alekseev-Meinrenken diffeomorphisms
Xiaomeng Xu ;
Date 16 Dec 2019
AbstractThe Riemann-Hilbert maps of certain meromorphic linear systems with Poncar$ m Acute{e}$ rank $1$ are diffeomorphisms $ u_u$, parametrized by the regular elements of a Cartan subalgebra $uinh_{ m reg}(mathbb{R})$ of $frak u(n)$, from the space $Herm(n)$ of $n imes n$ Hermitian matrices to the space $Herm^+(n)$ of $n imes n$ positive definite Hermitian matrices. In this paper, we propose an extension of the family of Riemann-Hilbert maps from $h_{ m reg}(mathbb{R})$ to its de Concini-Procesi wonderful compactification $mathcal{M}(mathbb{R})$ via isomonodromy deformation. We then study the map $ u_{rel}$ corresponding to a caterpillar point on $mathcal{M}(mathbb{R})$, and prove that (up to a gauge transformation) it coincides with the Alekseev-Meinrenken diffeomorphism $Gamma_{AM}$ from $Herm(n)$ to $Herm^+(n)$, a map uniquely characterized by distinguished linear algebra properties. We also discuss the applications of our results in Poisson geometry and representation theory.
Source arXiv, 1912.7196
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica