On the elliptic $\mathfrak{gl}_2$ solid-on-solid model: functional relations and determinants

TL;DR

This paper investigates an elliptic solid-on-solid model with domain-wall boundaries, revealing continuous families of determinantal representations for its partition function, parameterized by two arbitrary complex variables.

Contribution

It extends previous results by providing new continuous families of determinantal formulas for the model's partition function, highlighting their invariance under parameter choices.

Findings

Multiple continuous determinantal representations derived

Partition function remains invariant under parameter variations

Enhanced understanding of elliptic quantum group symmetries

Abstract

In this work we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group $\mathcal{E}_{p, \gamma}[\widehat{\mathfrak{gl}_2}]$ as its underlying symmetry algebra. We elaborate on results previously presented by the author and extend our analysis to include continuous families of single determinantal representations for the model's partition function. Interestingly, our families of representations are parameterized by two continuous complex variables which can be arbitrarily chosen without affecting the partition function.