http://imrp.oxfordjournals.org International Mathematics Research Papers - RSS feed of current issue 1687-3009 2008 International Mathematics Research Papers 1687-3017 http://imrp.oxfordjournals.org/cgi/content/short/2008/rpn009/rpn009?rss=1 The author, and independently, De Concini, conjectured that the monodromy of the Casimir connection of a simple Lie algebra is described by the quantum Weyl group operators of the quantum group . The aim of this article, and of its sequel [47], is to prove this conjecture. The proof relies upon the use of quasi-Coxeter algebras, which are to generalized braid groups what Drinfeld's quasitriangular quasibialgebras are to the Artin braid groups B_n. Using an appropriate deformation cohomology, we reduce the conjecture to the existence of a quasi-Coxeter, quasitriangular quasibialgebra structure on the enveloping algebra which interpolates between the quasi-Coxeter algebra structure underlying the Casimir connection, and the quasitriangular quasibialgebra structure underlying the Knizhnik–Zamolodchikov equations. The existence of this structure will be proved in [47].

]]> 2008-12-12 info:doi/10.1093/imrp/rpn009 Oxford University Press rpn009 2008 167 2008-12-12 rpn009 Research Articles