On fusion procedure for the two-parameter quantum algebra in type A

Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}({\mathfrak{s}\mathfrak{l}}_n)$ are explicitly constructed using the fusion procedure when $r{s}^{-1}$ is generic. This provides an alternative and combinatorial description of the Schur-Weyl duality for the two-parameter quantum linear algebras of type $A$.