2000/01/31 by Giovanni Felder, G. Felder, Yu. A. Markov +8
Chemistry · Mathematics · Physics and Astronomy · #17B10 #17B56 #33C80 #35Q40 #81R10 #Advanced Topics in Algebra #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B10 #msc:17B56 #msc:33C80 #msc:35Q40 #msc:81R10
paper · pdf · doi:10.48550/arxiv.math/0001184
34 pages, LaTeX
arxiv created 2000/01/31 · openalex publication_date 2000/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a system of "dynamical" differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables zi taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the "dual" variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions.