R-matrix and inverse Shapovalov form

TL;DR

This paper constructs the inverse Shapovalov form of a quantum group using its universal R-matrix, linking it to the ABRR equation for dynamical twist, advancing algebraic understanding.

Contribution

It introduces a novel method to derive the inverse Shapovalov form from the universal R-matrix, connecting it with the ABRR equation.

Findings

Explicit construction of the inverse Shapovalov form

Connection established between the R-matrix approach and ABRR equation

Advancement in algebraic structures of quantum groups

Abstract

We construct the inverse Shapovalov form of a simple complex quantum group from its universal R-matrix based on a generalized Nagel-Moshinsky approach to lowering operators. We establish a connection between this algorithm and the ABRR equation for dynamical twist.