The q-deformed Knizhnik-Zamolodchikov-Bernard heat equation

Abstract

We introduce a q-deformation of the genus one sl_2 Knizhnik-Zamolodchikov-Bernard heat equation. We show that this equation for the dependence on the moduli of elliptic curves is compatible with the qKZB equations, which give the dependence on the marked points.

18 pages, 1 figure, Latex. Revised and expanded version, with a new section on conformal blocks

References in corpus (4)

• The elliptic gamma function and SL(3,Z) x Z^3
• Multi-point Local Height Probabilities in the Integrable RSOS Model
• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Solutions of the elliptic qKZB equations and Bethe ansatz I

Cited by in corpus (8)

• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)
• Basic Properties of Non-Stationary Ruijsenaars Functions
• Multiplication Formulas for the Elliptic Gamma Function
• Traces of intertwiners for quantum affine sl_2 and Felder-Varchenko functions
• Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials
• Affine Macdonald conjectures and special values of Felder-Varchenko functions
• The orthogonality and qKZB-heat equation for traces of U_q(g)-intertwiners