Reflection matrices for the $U_{q}[spo(2n|2m)]$ vertex model

TL;DR

This paper classifies solutions to the graded reflection equations for the $U_{q}[spo(2n|2m)]$ vertex model, identifying twelve classes of reflection matrices with varying degrees of freedom, including diagonal and non-diagonal types.

Contribution

It provides a comprehensive classification of reflection matrices for the $U_{q}[spo(2n|2m)]$ vertex model, including explicit solutions and parameter counts.

Findings

Twelve classes of reflection matrices identified

Four classes are diagonal solutions

Non-diagonal matrices have parameters depending on bosonic and fermionic degrees of freedom

Abstract

We propose a classification of the solutions of the graded reflection equations to the $U_{q}[spo(2n|2m)]$ vertex model. We find twelve distinct classes of reflection matrices such that four of them are diagonal. In the non-diagonal matrices the number of free parameters depending on the number of bosonic ($2n$) and fermionic ($2m$) degrees of freedom while in the diagonal ones we find solutions with at most one free parameter.