Quasi-Coxeter quasitriangular quasibialgebras and the Casimir connection

2016/01/15 by Valerio Toledano-Laredo, Toledano-Laredo, Valerio
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.AG #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1601.04076

55 pages

arxiv created 2016/01/15 · arxiv updated 2016/01/19

Abstract

Let g be a complex, semisimple Lie algebra. We prove the existence of a quasi-Coxeter, quasitriangular quasibialgebra structure on the enveloping algebra of g, which binds the quasi-Coxeter structure underlying the Casimir connection of g and the quasitriangular quasibialgebra one underlying its KZ equations. This implies in particular that the monodromy of the rational Casimir connection of g is described by the quantum Weyl group operators of the quantum group U_h(g).

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