Hypergeometric Solutions of Trigonometric KZ Equations Satisfy Dynamical Difference Equations

✍ Scribed by Y. Markov; A. Varchenko

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 369 KB
• Volume: 166
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.2001.2027

✦ Synopsis

The trigonometric KZ equations associated to a Lie algebra g depend on a parameter l ¥ h where h … g is a Cartan subalgebra. A system of dynamical difference equations with respect to l compatible with the KZ equations is introduced by V. Tarasov and the second author (2000, Internat. Math. Res. Notices 15, 801-829). We prove that the standard hypergeometric solutions of the trigonometric KZ equations associated to sl N also satisfy the dynamical difference equations.