The trigonometric Casimir connection of a simple Lie algebra
arXiv:1003.2017 · doi:10.1016/j.jalgebra.2010.05.025
Abstract
Let g be a complex, semisimple Lie algebra, G the corresponding simply-connected Lie group and H a maximal torus in G. We construct a flat connection on H with logarithmic singularities on the root hypertori and values in the Yangian Y(g) of g. By analogy with the rational Casimir connection of g, we conjecture that the monodromy of this trigonometric connection is described by the quantum Weyl group operators of the quantum loop algebra U_h(Lg).
44 pages. Some typos corrected and minor changes made. Final version to appear in the Journal of Algebra