Knizhnik-Zamolodchikov type equations for the root system B and Capelli central elements

摘要

The construction of the well-known Knizhnik-Zamolodchikov equations uses the central element of the second order in the universal enveloping algebra for some Lie algebra. But in the universal enveloping algebra there exist central elements of higher orders. It seems desirable to use these elements for the construction of Knizhnik-Zamolodchikov type equations. In the present paper we give a construction of such Knizhnik-Zamolodchikov type equations for the root system B associated with Capelli central elements in the universal enveloping algebra for the orthogonal algebra.