The Two-parameter Quantum Supergroup Of Osp(1|2n) And Its Representations

We study the two-parameter quantum supergroup U_r,s(osp(1|2n)) corresponding to Lie superalgebra of osp(1|2n).We define two-parameter quantum supergroup U_r,s(osp(1|2n)) by generators and relations for the first time,together with the Z₂ graded Hopf algebra structure.We extend the definition of the Drinfel'd quantum double, and prove that U_r,s(osp(1|2n)) is isomorphic to the Drinfel'd quantum double D(B,B′) of the Z₂ graded Hopf subalgebras B and B′.Next,we give a detailed description of the commutative relations between integral basis elements of the two-parameter quantum supergroup U_r,s(osp(1|2n)), study the integrable representations,and then discuss the highest weight representations which are deformations of some U(osp(1|2n)) modules. Finally,we obtain both basis and center of U_r,s(osp(1|2)).