The factorized F-matrices for arbitrary U(1)^(N-1) integrable vertex models

TL;DR

This paper develops a general framework for factorized F-matrices in N-state vertex models with U(1) symmetries, providing explicit structures and applications to domain wall partition functions, especially for the N=3 case.

Contribution

It introduces a unitarity and Yang-Baxter based factorization for F-matrices in N-state models and conjectures their structure for the N=3 case, including explicit algebraic expressions.

Findings

Factorization of F-matrices based on unitarity and Yang-Baxter relations.

Explicit algebraic expressions for domain wall partition functions in N=3 models.

Identification of R-matrices on del Pezzo surfaces with general weights.

Abstract

We discuss the $F$-matrices associated to the $R$-matrix of a general $N$-state vertex model whose statistical configurations encode $N-1$ U(1) symmetries. The factorization condition is shown for arbitrary weights being based only on the unitarity property and the Yang-Baxter relation satisfied by the $R$-matrix. Focusing on the N=3 case we are able to conjecture the structure of some relevant twisted monodromy matrix elements for general weights. We apply this result providing the algebraic expressions of the domain wall partition functions built up in terms of the creation and annihilation monodromy fields. For N=3 we also exhibit a $R$-matrix whose weights lie on a del Pezzo surface and have a rather general structure.