Weight functions and Drinfeld currents

TL;DR

This paper constructs a universal weight function for untwisted quantum affine algebras, which is crucial for understanding Bethe vectors and solutions to qKZ equations in representation theory.

Contribution

It introduces a new construction of the universal weight function using projections onto Borel subalgebra intersections, expanding the theoretical framework.

Findings

Provides a new construction method for the universal weight function.

Analyzes the functional properties of the constructed weight function.

Enhances the understanding of off-shell Bethe vectors and qKZ solutions.

Abstract

A universal weight function for a quantum affine algebra is a family of functions with values in a quotient of its Borel subalgebra, satisfying certain coalgebraic properties. In representations of the quantum affine algebra it gives off-shell Bethe vectors and is used in the construction of solutions of the qKZ equations. We construct a universal weight function for each untwisted quantum affine algebra, using projections onto the intersection of Borel subalgebras of different types, and study its functional properties.