Doubling Operations and Monodromy of Generalized Knizhnik–Zamolodchikov Equations

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.