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 Tr. Mat. Inst. Steklova, 2002, Volume 236, Pages 218–225 (Mi tm292)

Doubling Operations and Monodromy of Generalized Knizhnik–Zamolodchikov Equations

V. P. Leksin

Kolomna State Pedagogical Institute

Abstract: The Knizhnik–Zamolodchikov (KZ) equations associated to root systems of $A$ and $B$ types are considered whose coefficients belong to the algebras of chord diagrams and symmetric chord diagrams, respectively. Explicit formulas for the monodromy of these equations are derived with the use of doubling operations in the algebras of chord diagrams. Reductions of the KZ equations with matrix coefficients to Schlesinger deformations are considered. The simplest solutions to the Schlesinger equations under such reductions are found.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 236, 206–213

Bibliographic databases:

UDC: 517.538+514

Citation: V. P. Leksin, “Doubling Operations and Monodromy of Generalized Knizhnik–Zamolodchikov Equations”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Tr. Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 218–225; Proc. Steklov Inst. Math., 236 (2002), 206–213

Citation in format AMSBIB
\Bibitem{Lek02} \by V.~P.~Leksin \paper Doubling Operations and Monodromy of Generalized Knizhnik--Zamolodchikov Equations \inbook Differential equations and dynamical systems \bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko \serial Tr. Mat. Inst. Steklova \yr 2002 \vol 236 \pages 218--225 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm292} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1931022} \zmath{https://zbmath.org/?q=an:1020.32008} \transl \jour Proc. Steklov Inst. Math. \yr 2002 \vol 236 \pages 206--213 

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This publication is cited in the following articles:
1. Golubeva V.A., “On the Riemann-Hilbert correspondence for generalized Knizhnik-Zamolodchikov equations for different root systems”, Differential Equations and Quantum Groups - ANDREY A. BOLIBRUKH MEMORIAL VOLUME, Irma Lectures in Mathematics and Theoretical Physics, 9, 2007, 189–207
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