Diagonalization of infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model

TL;DR

This paper develops a method to diagonalize the infinite transfer matrix of a boundary elliptic quantum group face model using free field realizations, advancing the understanding of integrable models with boundaries.

Contribution

It introduces a novel approach to diagonalize the infinite transfer matrix of the boundary $U_{q,p}(A_{N-1}^{(1)})$ face model via free field realizations.

Findings

Successfully diagonalized the infinite transfer matrix $T_B(z)$

Established a free field realization framework for boundary models

Enhanced understanding of boundary integrable systems

Abstract

We study infinitely many commuting operators $T_B(z)$, which we call infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model. We diagonalize infinite transfer matrix $T_B(z)$ by using free field realizations of the vertex operators of the elliptic quantum group $U_{q,p}(A_{N-1}^{(1)})$.