Reflection matrices for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model

TL;DR

This paper investigates the graded reflection equation for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model, classifying diagonal and non-diagonal solutions with varying free parameters based on bosonic and fermionic degrees of freedom.

Contribution

It provides a comprehensive classification of reflection matrices for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model, including new classes of solutions.

Findings

Four classes of diagonal solutions identified

Twelve classes of non-diagonal solutions found

Number of free parameters depends on bosonic and fermionic degrees

Abstract

The graded reflection equation is investigated for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model. We have found four classes of diagonal solutions with at the most one free parameter and twelve classes of non-diagonal ones with the number of free parameters depending on the number of bosonic ($r$) and fermionic ($2m$) degrees of freedom.