We provide a Faddeev-Reshetikhin-Takhtajan's RTT approach to the quantum group Fun(GL_{ r,s}(n)) and the quantum enveloping algebra U_{ r,s}(gl_n) corresponding to the two-parameter R-matrix. We prove that the quantum determinant det_{ r,s}T is a quasi-central element in Fun(GL_{ r,s}(n)) generalizing earlier results of Dipper-Donkin and Du-Parshall-Wang. The explicit formulation provides an interpretation of the deforming parameters, and the quantized algebra U_{ r,s}(R) is identified to U_{ r,s}(gl_n) as the dual algebra. We then construct n-1 quasi-central elements in U_{ r,s}(R) which are analogues of higher Casimir elements in U_q(gl_n).
Categories: math.QA math.RA