Difference Equations Compatible with Trigonometric Kz Differential Equations

Duality for Knizhinik-Zamolodchikov and Dynamical Equations, and Hypergeometric Integrals

The Knizhnik-Zamolodchikov (KZ ) equations is a holonomic system of differential equations for correlation functions in conformal field theory on the sphere [KZ]. The KZ equations play an important role in representation theory of affine Lie algebras and quantum groups, see for example [EFK]. There are rational, trigonometric and elliptic versions of KZ equations, depending on what kind of coef...

Daha and Bispectral Quantum Kz Equations

We use the double affine Hecke algebra of type GLN to construct an explicit consistent system of q-difference equations, which we call the bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik’s quantum affine KZ equations associated to principal series representations of the underlying affine Hecke algebra, a compatible system of q-difference equations ac...

Quantum Knizhnik-zamolodchikov Equations and Holomorphic Vector Bundles

Introduction In 1984 Knizhnik and Zamolodchikov [KZ] studied the matrix elements of intertwining operators between certain representations of affine Lie algebras and found that they satisfy a holonomic system of differential equations which are now called the Knizhnik-Zamolodchikov (KZ) equations. It turned out that the KZ equations (and hence, representation theory of affine Lie algebras) are ...

Differential Equations Compatible with KZ Equations

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.