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

TL;DR

This paper investigates the graded reflection equation for the $U_{q}[sl(r|2m)^{(2)}]$ vertex model, identifying multiple classes of solutions with varying free parameters based on bosonic and fermionic degrees of freedom.

Contribution

It classifies diagonal and non-diagonal solutions of the graded reflection equation for the $U_{q}[sl(r|2m)^{(2)}]$ vertex model, expanding understanding of boundary conditions.

Findings

Found four classes of diagonal solutions.

Identified twelve classes of non-diagonal solutions.

Number of free parameters varies with bosonic and fermionic degrees.

Abstract

The graded reflection equation is investigated for the $U_{q}[sl(r|2m)^{(2)}]$ vertex model. We have found four classes of diagonal solutions and twelve classes of non-diagonal ones. The number of free parameters for some solutions depends on the number of bosonic and fermionic degrees of freedom considered.