On integrability of a $q$-oscillator lattice with a $B$-boundary

TL;DR

This paper introduces a novel boundary transfer matrix for a $q$-oscillator lattice that generates integrals of motion and relates to a $3d$ reflection matrix, expanding understanding of integrable models without quantum group structures.

Contribution

It presents a new construction of a boundary transfer matrix for a $q$-oscillator lattice, providing integrals of motion and linking to a $3d$ reflection matrix, without relying on quantum group interpretation.

Findings

The transfer matrix produces a complete set of integrals of motion.

It relates to the $3d$ Kuniba-Okado reflection matrix.

The model lacks a quantum group interpretation.

Abstract

In this paper we propose a method of construction of a double layer-to-layer auxiliary transfer matrix defined on a half-plane with a boundary. The transfer matrix obtained has the following features: - It produces a complete set of integrals of motion, - Its ingredients can be seen as an auxiliary problem for $3d$ Kuniba-Okado reflection matrix, - The model obtained has no quantum group interpretation.