The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model

TL;DR

This paper uncovers an $L( ext{sl}_2)$ symmetry in a specific sector of the Bazhanov-Stroganov model, linking it to the superintegrable chiral Potts model through polynomial equivalence, revealing deep algebraic structures.

Contribution

It demonstrates the presence of $L( ext{sl}_2)$ symmetry in the Bazhanov-Stroganov model and connects its eigenspaces to the spectrum of the superintegrable chiral Potts model.

Findings

Identification of $L( ext{sl}_2)$ symmetry in the model

Equivalence of Drinfeld polynomial with chiral Potts polynomial

Link between algebraic structures and Ising-like spectrum

Abstract

The loop algebra $L(\mathfrak{sl}_{2})$ symmetry is found in a sector of the nilpotent Bazhanov-Stroganov model. The Drinfeld polynomial of a $L(\mathfrak{sl}_{2})$-degenerate eigenspace of the model is equivalent to the polynomial which characterizes a subspace with the Ising-like spectrum of the superintegrable chiral Potts model.