TL;DR
This paper explores the construction of integrable boundary conditions in supersymmetric quantum models, deriving conditions for various types of reflection matrices and focusing on models with gl(m|n) symmetry.
Contribution
It introduces a systematic method for constructing bosonic, fermionic, and mixed reflection matrices in supersymmetric models with gl(m|n) symmetry.
Findings
Derived conditions for purely bosonic, fermionic, and mixed reflection matrices.
Constructed explicit bosonic reflection matrices for general m, n.
Provided a framework for building full reflection matrices with fermionic components.
Abstract
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 gl(m|n) or Uq(gl(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.
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