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Article overview
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Irregular Riemann-Hilbert correspondence, Alekseev-Meinrenken dynamical r-matrix and Drinfeld twist | Xiaomeng Xu
; | Date: |
26 Jul 2015 | Abstract: | In 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 | Services: | Forum | Review | PDF | Favorites |
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