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Dynamical Differential Equations Compatible with Rational <Emphasis Type="Italic">qKZ</Emphasis> Equations

Authors:	V?Tarasov vtarasov@mathiupuiedu" title="vt@pdmirasru Email author" target="_blank">vtarasov@mathiupuiedu" itemprop="email" data-track="click" data-track-action="Email author" data-track-label="">Email author A?Varchenko

Institution:	(1) St. Petersburg Branch of Steklov Mathematical Institute, St. Petersburg, Fontanka 27, 191023, Russia;(2) Department of Mathematical Sciences, Indiana University Purdue University at Indianapolis, Indianapolis, 46202, IN, USA;(3) Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, 27599, NC, USA

Abstract:	For the Lie algebra $\cal{g l}$ _N we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $\cal{g l}$ _N rational quantized Knizhnik–Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the $\cal{g l}$ _N Weyl group.Mathematics Subject Classifications (2000). 17B37, 17B80, 81R10.

Keywords:	Knizhnik– Zamolodchikov equations dynamical differential equations
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