Some eigenstates for a model associated with solutions of tetrahedron equation. II. A bit of algebraization

TL;DR

This paper enhances the understanding of eigenstates in a tetrahedron equation-based model by introducing an algebraic construction of one-particle states and identifying string solutions as symmetries of the transfer matrix.

Contribution

It presents a more algebraic approach to constructing eigenstates and clarifies the role of string solutions as symmetries, advancing the algebraic understanding of the model.

Findings

Existence of an algebraic construction for one-particle states.

Strings are symmetries of the transfer matrix.

Improved algebraic framework for the model.

Abstract

This paper adds two observations to the work solv-int/9701016 where some eigenstates for a model based on tetrahedron equation have been constructed. The first observation is that there exists a more "algebraic" construction of one-particle states, resembling the 1+1-dimensional algebraic Bethe ansatz. The second observation is that the strings introduced in solv-int/9701016 are symmetries of a transfer matrix, rather than just eigenstates.