Finite-dimensional representations of U q (osp(1/2n)) and its connection with quantum so(2n+1)

It is shown that the quantum supergroup U_q(osp(1/2_n)) is essentially isomorphic to the quantum group U_-q(so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U_q(osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.