2017/01/27 by Xiaomeng Xu, Xu, Xiaomeng
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.QA #math.SG
paper · pdf · doi:10.48550/arxiv.1701.08113
21pages
arxiv created 2017/01/27 · openalex publication_date 2017/01/27 · arxiv updated 2017/01/30 · openalex created_date 2017/02/10 · openalex updated_date 2026/07/28
In 2007, Alekseev-Meinrenken proved that there exists a Ginzburg-Weinstein diffeomorphism from the dual Lie algebra \rm u(n)^* to the dual Poisson Lie group U(n)^* compatible with the Gelfand-Zeitlin integrable systems. In this paper, we explicitly construct such diffeomorphisms via Stokes phenomenon and Boalch's dual exponential maps. Then we introduce a relative version of the Ginzburg-Weinstein linearization motivated by irregular Riemann-Hilbert correspondence, and generalize the results of Enriquez-Etingof-Marshall to this relative setting. In particular, we prove the connection matrix for a certain irregular Riemann-Hilbert problem satisfies a relative gauge transformation equation of the Alekseev-Meinrenken dynamical r-matrices. This gauge equation is then derived as the semiclassical limit of the relative Drinfeld twist equation.