Geodesic
Doubling Operations and Monodromy of Generalized Knizhnik--Zamolodchikov Equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 218-225

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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. 
@article{TM_2002_236_a22,
     author = {V. P. Leksin},
     title = {Doubling {Operations} and {Monodromy} of {Generalized} {Knizhnik--Zamolodchikov} {Equations}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {218--225},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a22/}
}
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V. P. Leksin. Doubling Operations and Monodromy of Generalized Knizhnik--Zamolodchikov Equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 218-225. http://geodesic.mathdoc.fr/item/TM_2002_236_a22/