Root of unity symmetries in the 8 and 6 vertex models

TL;DR

This paper reviews the symmetries of the 8 and 6 vertex models at roots of unity, linking them to affine Lie algebra representations, Drinfeld polynomials, and Bethe vectors.

Contribution

It elucidates the connection between root of unity symmetries in vertex models and advanced algebraic structures, providing a comprehensive theoretical framework.

Findings

Identifies new symmetries at roots of unity in vertex models

Connects these symmetries to affine Lie algebra representations

Relates symmetries to Drinfeld polynomials and Bethe vectors

Abstract

We review the recently discovered symmetries of the 8 and 6 vertex models which exist at roots of unity and present their relation with representation theory of affine Lie algebras, Drinfeld polynomials and Bethe vectors.