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2009 | 7 | 1 | 145-162
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On the solutions of Knizhnik-Zamolodchikov system

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of the KZ system is rational too. We give the method of constructing the corresponding rational solution. We deduce the asymptotic formulas for the solution of the KZ system when the parameter ρ is an integer.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
1
Strony
145-162
Opis fizyczny
Daty
wydano
2009-03-01
online
2009-01-10
Bibliografia
  • [1] Bateman H., Erdely A., Higher transcendental functions 1, New York, 1953
  • [2] Burrow M., Representation theory of finite groups, Academic Press, New York-London, 1965
  • [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] Felder G., Veselov A., Polynomial solutions of the Knizhnik-Zamolodchikov equations and Schur-Weyl duality, Int. Math. Res. Not. IMRN, 2007, 15, 1–27
  • [5] Matsuo A., An application of Aomoto-Gelfand hypergeometric functions to the SU(n) Knizhnik-Zamolodchikov equation. Comm. Math. Phys., 1990, 134, 65–77 http://dx.doi.org/10.1007/BF02102089[Crossref]
  • [6] Sakhnovich L.A., Spectral theory of canonical differential systems. Method of operator identities, Operator Theory: Advances and Applications 107, Birkhäuser Verlag, Basel, 1999
  • [7] Sakhnovich L.A., Meromorphic solutions of linear differential systems, Painleve type functions, Oper. Matrices, 2007, 1, 87–111
  • [8] Sakhnovich L.A., Explicit rational solutions of Knizhnik-Zamolodchikov equation, Cent. Eur. J. Math., 2008, 6, 179–187 http://dx.doi.org/10.2478/s11533-008-0013-0[Crossref]
  • [9] Sakhnovich L.A., Rational solutions of KZ equation, Existence and construction, preprint available at arXiv.math:- ph/0609067
  • [10] Sakhnovich L.A., Rational solutions of KZ equation, Case S4, preprint available at arXiv:math.CA/0702404
  • [11] Tydnyuk A., Rational solution of KZ equation, preprint available at arXiv:math/0162153
  • [12] Tydnyuk A., Explicit rational solution of KZ equation, preprint available at arXiv:math/07091141
  • [13] Varchenko A., Asymptotic solutions of Knizhnik-Zamolodchikov equation and crystal base, Comm. Math. Phys., 1995, 171, 99–137 http://dx.doi.org/10.1007/BF02103772[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0059-z
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