Reflection matrices with $U_q[osp^{(2)}(2|2m)]$ symmetry

TL;DR

This paper classifies reflection matrices for a specific quantum superalgebra vertex-model, identifying four families of solutions including complete, block-diagonal, X-shape, and diagonal types, with some solutions applicable to related models.

Contribution

It provides a comprehensive classification of reflection K-matrices for the $U_q[osp^{(2)}(2|2m)]$ vertex-model, introducing four distinct solution families and extending diagonal solutions to related models.

Findings

Identified four families of reflection K-matrices.

Found complete, block-diagonal, X-shape, and diagonal solutions.

Diagonal solutions also apply to related $U_q[D^{(2)}]$ models.

Abstract

We propose a classification of the reflection $K$-matrices (solutions of the boundary Yang-Baxter equation) for the $U_{q}[\mathrm{osp}^{\left(2\right)}\left(2|2m\right)]=U_{q}[C^{\left(2\right)}\left(m+1\right)]$ vertex-model. We have found four families of solutions, namely, the complete solutions, in which no elements of the reflection $K$-matrix is null, the block-diagonal solutions, the $X$-shape solutions and the diagonal solutions. We highlight that these diagonal $K$-matrices also hold for the $U_{q}[\mathrm{osp}^{\left(2\right)}\left(2n+2|2m\right)]=U_{q}[D^{\left(2\right)}\left(n+1,m\right)]$ vertex-model.