A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain. II. The Polynomials $p_n$

TL;DR

This paper explores the connection between specialized partition functions of the 8VSOS model and polynomials related to the supersymmetric XYZ spin chain, extending previous work on similar polynomials and their conjectured identities.

Contribution

It establishes a link between the 8VSOS model's partition function and polynomials $p_n(z)$, contributing to the understanding of eigenvectors in the supersymmetric XYZ spin chain.

Findings

Connection between 8VSOS model and polynomials $p_n(z)$

Polynomials $p_n(z)$ conjectured to match Bazhanov and Mangazeev's polynomials

Extension of previous work on polynomials $q_n(z)$

Abstract

By specializing the parameters in the partition function of the 8VSOS model with domain wall boundary conditions and diagonal reflecting end, we find connections between the three-color model and certain polynomials $p_n(z)$, which are conjectured to be equal to certain polynomials of Bazhanov and Mangazeev, appearing in the eigenvectors of the Hamiltonian of the supersymmetric XYZ spin chain. This article is a continuation of a previous paper where we investigated the related polynomials $q_n(z)$, also conjectured to be equal to polynomials of Bazhanov and Mangazeev, appearing in the eigenvectors of the supersymmetric XYZ spin chain.