Vertex operators for boundary algebras

TL;DR

This paper develops a method to embed boundary algebras into ZF algebras using vertex operators, linking different approaches to quantum integrable systems with boundaries, applicable to a wide class of quantum groups.

Contribution

It introduces a new embedding construction of boundary algebras into ZF algebras using well-bred vertex operators classified by reflection matrices.

Findings

Provides a general embedding method based on R-matrix unitarity.

Connects boundary algebra approaches to bulk systems in quantum integrable models.

Applicable to any infinite dimensional quantum group.

Abstract

We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to make the link between different approaches of the systems with boundaries. The construction uses the well-bred vertex operators built recently, and is classified by reflection matrices. It relies only on the existence of an R-matrix obeying a unitarity condition, and as such can be applied to any infinite dimensional quantum group.