# Explicit rational solutions of Knizhnik-Zamolodchikov equation

Open Mathematics (2008)

- Volume: 6, Issue: 1, page 179-187
- ISSN: 2391-5455

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topLev Sakhnovich. "Explicit rational solutions of Knizhnik-Zamolodchikov equation." Open Mathematics 6.1 (2008): 179-187. <http://eudml.org/doc/269331>.

@article{LevSakhnovich2008,

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.},

author = {Lev Sakhnovich},

journal = {Open Mathematics},

keywords = {Symmetric group; natural representation; linear differential system; rational fundamental solution},

language = {eng},

number = {1},

pages = {179-187},

title = {Explicit rational solutions of Knizhnik-Zamolodchikov equation},

url = {http://eudml.org/doc/269331},

volume = {6},

year = {2008},

}

TY - JOUR

AU - Lev Sakhnovich

TI - Explicit rational solutions of Knizhnik-Zamolodchikov equation

JO - Open Mathematics

PY - 2008

VL - 6

IS - 1

SP - 179

EP - 187

AB - 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.

LA - eng

KW - Symmetric group; natural representation; linear differential system; rational fundamental solution

UR - http://eudml.org/doc/269331

ER -

## References

top- [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 Zbl0903.17006
- [4] Sakhnovich L.A., Meromorphic solutions of linear differential systems Painleve type functions, Oper. Matrices, 2007, 1, 87–111 Zbl1114.34068
- [5] Sakhnovich L.A., Rational solutions of Knizhnik-Zamolodchikov system, preprint avaiable at http://arxiv.org/abs/math-ph/0609067 Zbl1153.34054
- [6] Sakhnovich L.A., Rational solution of KZ equation case ${\mathcal{S}}_{4}$ 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 Zbl0729.35129
- [8] Tydnyuk A., Explicit rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/0709.1141

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