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

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