RIGIDITY THEOREMS FOR MULTIPARAMETRIC DEFORMATIONS OF ALGEBRAIC STRUCTURES, ASSOCIATED WITH THE KNIZHNIK-ZAMOLODCHIKOV EQUATIONS

摘要

The paper is concerned to a version of the multidimensional Riemann-Hilbert problem in the class of Knizhnik-Zamolod-chikov (KZ) equations associated with root systems, more exactly, to the extension of the Drinfeld-Kohno theorem proved for the KZ equation of the type A{sub}(n-1) to the generalized KZ equation associated with the root system B{sub}n. The rigidity theorems for the corresponding braided quasi-bialgebra structures connected with two-parametric deformations of the universal enveloping algebra for the Lie algebra of B{sub}n type are proved. In the proof the cyclic cohomology is used.