# Boundary Algebraic Bethe Ansatz for a nineteen vertex model with $U_{q}[\mathrm{osp}(2|2)^{(2)}]$ symmetry

## TL;DR

This paper develops a boundary algebraic Bethe Ansatz for a supersymmetric nineteen vertex model with $U_{q}[osp(2|2)^{(2)}]$ symmetry, deriving eigenvalues, eigenvectors, and Bethe equations.

## Contribution

It introduces a novel boundary algebraic Bethe Ansatz approach for a specific supersymmetric vertex model with twisted quantum affine Lie superalgebra symmetry.

## Key findings

- Eigenvalues and eigenvectors of the transfer matrix are explicitly calculated.
- Bethe Ansatz equations for the model are derived.
- The method applies to models with diagonal reflection K-matrices.

## Abstract

The boundary algebraic Bethe Ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra $U_{q}[\mathrm{osp}(2|2)^{(2)}]$ is presented. The eigenvalues and eigenvectors of Sklyanin's transfer matrix, with diagonal reflection $K$-matrices, are calculated and the corresponding Bethe Ansatz equations are obtained.