Quantum Supergroup $U_{r,s}(osp(1,2))$, Scasimir Operators, and Dickson polynomials

We study the center of the two-parameter quantum supergroup $U_{r,s}(osp(1,2))$ using the Dickson polynomial. We show that the Scasimir operator is completely determined by the $q$-deformed Chebychev polynomial, generalizing an earlier work of Arnaudon and Bauer.