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

Abstract

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 τ,γ (gl 3 ) to introduce an elliptic analogue of the partition functions associated with E τ,γ (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.