Representations of quantum superalgebra $U_{r,s}(\mathrm{o}\mathrm{s}\mathrm{p}(1,2))$ at the root of unity and its restrictions

In this paper, the simple modules for the quantum superalgebra $U_{r,s}(\mathrm{o}\mathrm{s}\mathrm{p}(1,2))$ with two parameters at the root of unity (i.e., $q=(r{s}^{-1}{)}^{1/2}$ is a root of unity) are completely determined up to isomorphism. Furthermore, the classification of finite-dimensional simple modules over the restricted quantum superalgebra ${\overline{U}}_{r,s}(\mathrm{o}\mathrm{s}\mathrm{p}(1,2))$ is given.