Integral solutions of trigonometric Knizhnik-Zamolodchikov equations and Kac-Moody algebras

DOI10.2977/prims/1195169269zbMath0753.17036OpenAlexW2023827071MaRDI QIDQ1187162

Ivan V. Cherednik

Publication date: 28 June 1992

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195169269

zbMATH Keywords

\(\tau\)-functionsKnizhnik-Zamolodchikov equationhypergeometric solutionshypergeometrie functions

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Applications of Lie (super)algebras to physics, etc. (17B81) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (16)

Representations of affine Lie algebras, parabolic differential equations, and Lamé functions ⋮ KNIZHNIK–ZAMOLODCHIKOV–BERNARD EQUATIONS CONNECTED WITH THE EIGHT-VERTEX MODEL ⋮ Gaudin model, Bethe ansatz and critical level ⋮ Vector version of Matsuo-Cherednik equation for the root system \(G_ 2\) ⋮ \(\text{sl}(2| 1)^{(2)}\) Gaudin magnet and its associated Knizhnik--Zamolodchikov equation ⋮ Unitarity of the KZ/Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras ⋮ Quantum affine algebras and holonomic difference equations ⋮ Topological representations of quantum groups and conformal field theory ⋮ Quantum Knizhnik-Zamolodchikov equations and affine root systems ⋮ Jackson integrals of Jordan-Pochhammer type and quantum Knizhnik-Zamolodchikov equations ⋮ Integrable connections related to zonal spherical functions ⋮ Off-shell Bethe ansatz equation for \(\text{osp}(2|1)\) Gaudin magnets ⋮ Deformations of \(W\)-algebras associated to simple Lie algebras ⋮ Quantum algebra structure of certain Jackson integrals ⋮ Hypergeometric solutions of trigonometric KZ equations satisfy dynamical difference equations ⋮ Representations of affine Lie algebras, elliptic \(r\)-matrix systems, and special functions

Cites Work

• An application of Aomoto-Gelfand hypergeometric functions to the SU(n) Knizhnik-Zamolodchikov equation
• Definition of functions for generalized affine Lie algebras
• Infinite dimensional Lie algebras. An introduction
• Functional realization of basic representations of factorizable Lie groups and algebras
• Current algebras and Wess-Zumino model in two dimensions
• HYPERGEOMETRIC-TYPE INTEGRALS AND THE $\mathfrak{sl}(2, {\rm C})$ KNIZHNIK-ZAMOLODCHIKOV EQUATION
• Solutions of the classical Yang-Baxter equation for simple Lie algebras

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