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In \cite{fl}, the authors get a new presentation of two-parameter quantumalgebra $U_{v,t}(\mathfrak{g})$. Their presentation can cover all Kac-Moodycases. In this paper, we construct a suitable Hopf pairing such that$U_{v,t}(sl_{n})$ can be realized as Drinfeld double of certain Hopfsubalgebras with respect to the Hopf pairing. Using Hopf pairing, we constructa $R$-matrix for $U_{v,t}(sl_{n})$ which will be used to give the Schur-Weyldual between $U_{v,t}(sl_{n})$ and Hecke algebra $H_{k}(v,t)$. Furthermore,using the Fusion procedure we construct the primitive orthogonal idempotents of$H_{k}(v,t)$. As a corollary, we give the explicit construction of irreducible$U_{v,t}(sl_{n})$-representations of $V^{\otimes k}$.

Schur-Weyl duality for $U_{v,t}(sl_{n})$