On representations of $U_q^{\mathrm{\prime }}s{o}_n$

We study representations of the non-standard quantum deformation $U_q^{\mathrm{\prime }}s{o}_n$ of $Us{o}_n$ via a Verma module approach. This is used to recover the classification of finite-dimensional modules for $q$ not a root of unity, given by classical and non-classical series. We obtain new results at roots of unity, in particular for self-adjoint representations on Hilbert spaces.