The graded reflection equation is investigated for the U q [ osp ( r |2 m ) (1) ] vertex model. We have found diagonal solutions with at the most one free parameter and non-diagonal solutions with the number of free parameters depending on the number of bosonic ( r ) and fermionic (2 m ) degrees of freedom.
We consider the insertion of integrable boundaries for a class of supersymmetric quantum models. The generic conditions for constructing purely bosonic, purely fermionic or mixed type solutions of the graded reflection equation are extracted. Focusing on models associated with g l ( m | n ) or 𝒰 q ( g l ( m | n )) symmetry, we first consider purely bosonic reflection matrices with special structures, for general values of m , n . These solutions provide the bosonic parts to construct fuller reflection matrices, containing fermionic degrees of freedom as well.