Stokes phenomena, Poisson-Lie groups and quantum groups
Quantum Algebra
2022-03-15 v2 Algebraic Geometry
Differential Geometry
Representation Theory
Abstract
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 U_hg (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 U_hg is a Stokes matrix for the dynamical KZ equations.
Cite
@article{arxiv.2202.10298,
title = {Stokes phenomena, Poisson-Lie groups and quantum groups},
author = {V. Toledano-Laredo and X. Xu},
journal= {arXiv preprint arXiv:2202.10298},
year = {2022}
}
Comments
Minor revisions. Submitted version. 27 pages