Quasi-Coxeter quasitriangular quasibialgebras and the Casimir connection

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).

55 pages

References in corpus (3)

• On the dynamical Yang-Baxter equation
• Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra
• Uniqueness of Coxeter structures on Kac-Moody algebras

Cited by in corpus (8)

• Crystals and monodromy of Bethe vectors
• Uniqueness of Coxeter structures on Kac-Moody algebras
• Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra
• Regularized limits of Stokes matrices, isomonodromy deformation and crystal basis
• Representations of quantum groups arising from the Stokes phenomenon
• Frobenius manifolds and quantum groups
• Irregular Riemann-Hilbert correspondence, Alekseev-Meinrenken dynamical r-matrices and Drinfeld twists
• Stokes phenomenon, Gelfand-Zeitlin systems and relative Ginzburg-Weinstein linearization