Dynamical differential equations compatible with rational qKZ equations

Abstract

For the Lie algebra $g{l}_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $g{l}_N$ rational quantized Knizhnik-Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the $g{l}_N$ Weyl group.

7 pages, AmsLaTeX

References in corpus (1)

• Geometry of q-Hypergeometric Functions as a Bridge between Yangians and Quantum Affine Algebras

Cited by in corpus (5)

• Bethe eigenvectors of higher transfer matrices
• The trigonometric Casimir connection of a simple Lie algebra
• 3d Mirror Symmetry for Instanton Moduli Spaces
• Toroidal q-Opers
• Degeneration of trigonometric dynamical difference equations for quantum loop algebras to trigonometric Casimir equations for Yangians