Explicit rational solutions of Knizhnik-Zamolodchikov equation

• Autorzy: Lev Sakhnovich
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 34M05: Entire and meromorphic solutions
• 47B38: Operators on function spaces (general)
• 34M55: Painlev\'e and other special equations; classification, hierarchies;

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 1
• Strony: 179-187

Daty

wydano

2008-03-01

online

2008-02-26

Twórcy

autor

Lev Sakhnovich

Bibliografia

• [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
• [4] Sakhnovich L.A., Meromorphic solutions of linear differential systems Painleve type functions, Oper. Matrices, 2007, 1, 87–111
• [5] Sakhnovich L.A., Rational solutions of Knizhnik-Zamolodchikov system, preprint avaiable at http://arxiv.org/abs/math-ph/0609067
• [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
• [8] Tydnyuk A., Explicit rational solution of the KZ equation (example), preprint avaiable at http://arxiv.org/abs/0709.1141

Identyfikatory

DOI

10.2478/s11533-008-0013-0