Stokes phenomena, Poisson-Lie groups and quantum groups

Autor:	Toledano-Laredo, V., Xu, X.
Rok vydání:	2022
Předmět:	Mathematics - Quantum Algebra Mathematics - Algebraic Geometry Mathematics - Differential Geometry Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: Minor revisions. Submitted version. 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.10298 Zobrazit plný text záznamu View this record from Arxiv