Dynamical Differential Equations Compatible with Rational qKZ Equations

Dynamical Differential Equations Compatible with Rational Qkz Equations

For the Lie algebra glN we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the glN rational quantized Knizhnik-Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the glN Weyl group. ∗ Department of Mathematical Sciences, Indiana Uni...

Differential Equations Compatible with Boundary Rational Qkz Equation

We give differential equations compatible with the rational qKZ equation with boundary reflection. The total system contains the trigonometric degeneration of the bispectral qKZ equation of type (C n , Cn) which in the case of type GLn was studied by van Meer and Stokman. We construct an integral formula for solutions to our compatible system in a special case.

Differential Equations Compatible with KZ Equations

Difference Equations Compatible with Trigonometric Kz Differential Equations

The trigonometric KZ equations associated with a Lie algebra g depend on a parameter λ ∈ h where h ⊂ g is the Cartan subalgebra. We suggest a system of dynamical difference equations with respect to λ compatible with the KZ equations. The dynamical equations are constructed in terms of intertwining operators of g -modules.

Differential Constraints Compatible with Linearized Equations

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints. One of the standard ways for determining particular solutions to partial differential equations is to reduce them to ordinary differential equations which are easier to solve. The classical work of Lie abo...