The trigonometric Casimir connection of a simple Lie algebra

Understand

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).