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

TL;DR

This paper develops new Knizhnik-Zamolodchikov type equations for root system B by utilizing higher-order Capelli central elements in the universal enveloping algebra of orthogonal Lie algebras.

Contribution

It introduces a novel construction of KZ-type equations based on higher-order Capelli central elements for root system B.

Findings

Constructed KZ-type equations for root system B.

Connected Capelli central elements to these equations.

Extended the framework of KZ equations beyond second order.

Abstract

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 are 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.