The trigonometric Casimir connection of a simple Lie algebra

Let g be a complex, semisimple Lie algebra, G the corresponding simply-connected Lie group and H subset of G a maximal torus. 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 (L-g). (C) 2010 Elsevier Inc. All rights reserved.