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29 March 2024
 
  » arxiv » 1507.7149

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Irregular Riemann-Hilbert correspondence, Alekseev-Meinrenken dynamical r-matrix and Drinfeld twist
Xiaomeng Xu ;
Date 26 Jul 2015
AbstractIn 2004, Enriquez-Etingof-Marshall suggested a new approach to the Ginzburg-Weinstein linearization theorem. This approach is based on solving a system of PDEs for a gauge transformation between the standard classical r-matrix and the Alekseev-Meinrenken dynamical r-matrix. In this paper, we explain that this gauge transformation can be constructed as a monodromy (connection matrix) for a certain irregular Riemann-Hilbert problem. This further indicates a surprising relation between the connection matrix and Drinfeld twist. Our construction is based on earlier works by Boalch. As byproducts, we get a symplectic neighborhood version of the Ginzburg-Weinstein linearization theorem as well as a new description of the Lu-Weinstein symplectic double.
Source arXiv, 1507.7149
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