Abstract
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group \( \mathcal{S}_n \) n . We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Burrow M., Representation theory of finite groups, Academic Press, New York-London, 1965
Chervov A., Talalaev D., Quantum spectral curves quantum integrable systems and the geometric Langlands correspondence, preprint avaiable at http://arxiv.org/abs/hep-th/0604128
Etingof P.I., Frenkel I.B., Kirillov A.A.(jr.), Lectures on representation theory and Knizhnik-Zamolodchikov equations, Mathematical Surveys and Monographs 58, American Mathematical Society, Providence, RI, 1998
Sakhnovich L.A., Meromorphic solutions of linear differential systems Painleve type functions, Oper. Matrices, 2007, 1, 87–111
Sakhnovich L.A., Rational solutions of Knizhnik-Zamolodchikov system, preprint avaiable at http://arxiv.org/abs/math-ph/0609067
Sakhnovich L.A., Rational solution of KZ equation case \( \mathcal{S}_4 \) 4, preprint avaiable at http://arxiv.org/abs/math/0702404
Tydnyuk A., Rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/math/0612153
Tydnyuk A., Explicit rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/0709.1141
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Sakhnovich, L. Explicit rational solutions of Knizhnik-Zamolodchikov equation. centr.eur.j.math. 6, 179–187 (2008). https://doi.org/10.2478/s11533-008-0013-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11533-008-0013-0