A class of partition functions associated with $E_{τ,γ}(gl_3)$ by Izergin-Korepin analysis

Kohei Motegi

Published 2019-09-16Version 1

Recently, a class of partition functions associated with higher rank rational and trigonometric integrable models were introduced by Foda and Manabe. We use the dynamical $R$-matrix of the elliptic quantum group $E_{\tau,\gamma}(gl_3)$ to introduce an elliptic analogue of the partition functions associated with $E_{\tau,\gamma}(gl_3)$. We investigate the partition functions of Foda-Manabe type by developing a nested version of the elliptic Izergin-Korepin analysis, and present the explicit forms as symmetrization of multivariable elliptic functions.