2022/02/21 by Valerio Toledano-Laredo, X. Xu, Toledano-Laredo, V. +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2202.10298
openalex publication_date 2022/02/21 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Let g be a complex semisimple Lie algebra, G the simply-connected Poisson-Lie group corresponding to g, and G* its dual. G-valued Stokes phenomena were used by Boalch [Bo1,Bo2] to give a canonical, analytic linearisation of the Poisson structure on G*. Ug-valued Stokes phenomena were used by the first author to construct a twist killing the KZ associator, and therefore give a transcendental construction of the Drinfeld-Jimbo quantum group Uhg (arXiv:1601.04076). In the present paper, we show that the former construction can be obtained as semiclassical limit of the latter. Along the way, we also show that the R-matrix of Uhg is a Stokes matrix for the dynamical KZ equations.