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 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.
@article{bwmeta1.element.doi-10_2478_s11533-008-0013-0,
author = {Lev Sakhnovich},
title = {Explicit rational solutions of Knizhnik-Zamolodchikov equation},
journal = {Open Mathematics},
volume = {6},
year = {2008},
pages = {179-187},
zbl = {1153.34054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0013-0}
}
Lev Sakhnovich. Explicit rational solutions of Knizhnik-Zamolodchikov equation. Open Mathematics, Tome 6 (2008) pp. 179-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0013-0/
[1] Burrow M., Representation theory of finite groups, Academic Press, New York-London, 1965
[2] 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
[3] 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 | Zbl 0903.17006
[4] Sakhnovich L.A., Meromorphic solutions of linear differential systems Painleve type functions, Oper. Matrices, 2007, 1, 87–111 | Zbl 1114.34068
[5] Sakhnovich L.A., Rational solutions of Knizhnik-Zamolodchikov system, preprint avaiable at http://arxiv.org/abs/math-ph/0609067 | Zbl 1153.34054
[6] Sakhnovich L.A., Rational solution of KZ equation case 4, preprint avaiable at http://arxiv.org/abs/math/0702404
[7] Tydnyuk A., Rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/math/0612153 | Zbl 0729.35129
[8] Tydnyuk A., Explicit rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/0709.1141