Scasimir operator, Scentre and Representations of U_q(osp(1|2))

A bosonic operator of U_q(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of U_q(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the classical case, it also simplifies the classification of finite dimensional irreducible representations.