Explicit rational solutions of Knizhnik-Zamolodchikov equation

Lev Sakhnovich

Open Mathematics (2008)

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

Abstract

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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 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.

How to cite

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Lev 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

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  1. [1] Burrow M., Representation theory of finite groups, Academic Press, New York-London, 1965 
  2. [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. [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. [4] Sakhnovich L.A., Meromorphic solutions of linear differential systems Painleve type functions, Oper. Matrices, 2007, 1, 87–111 Zbl1114.34068
  5. [5] Sakhnovich L.A., Rational solutions of Knizhnik-Zamolodchikov system, preprint avaiable at http://arxiv.org/abs/math-ph/0609067 Zbl1153.34054
  6. [6] Sakhnovich L.A., Rational solution of KZ equation case 𝒮 4 4, preprint avaiable at http://arxiv.org/abs/math/0702404 
  7. [7] Tydnyuk A., Rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/math/0612153 Zbl0729.35129
  8. [8] Tydnyuk A., Explicit rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/0709.1141 

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