R-matrix realization of two-parameter quantum group Uᵣ,ₛ(glₙ)

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We provide a Faddeev-Reshetikhin-Takhtajan's RTT approach to the quantum group Fun(GLᵣ,ₛ(n)) and the quantum enveloping algebra Uᵣ,ₛ(glₙ) corresponding to the two-parameter R-matrix. We prove that the quantum determinant detᵣ,ₛT is a quasi-central element in Fun(GLᵣ,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 Uᵣ,ₛ(R) is identified to Uᵣ,ₛ(glₙ) as the dual algebra. We then construct n-1 quasi-central elements in Uᵣ,ₛ(R) which are analogues of higher Casimir elements in Uq(glₙ).