Geometric Schur Duality of two parameter quantum group of type A

In this paper, we give an geometric description of the Schur-Weyl duality for two-parameter quantum algebras $U_{v,t}(g{l}_n)$, where $U_{v,t}(g{l}_n)$ is the deformation of $U_v(I,\cdot )$, the classic Shur-Weyl duality $(U_{r, s}(gl_n), V^{\otimes d}, H_d(r, s))$canbeseenasacorollaryoftheShur-Weylduality$(U_{v, t}(gl_n), V^{\otimes d}, H_d(v, t))$ by using the galois descend approach. we also establish the Shur-Weyl duality between the algebras $\widetilde{U_{v,t}(g{l}_N{)}^m}$, $\widehat{U_{v,t}(g{l}_N{)}^m}$ and Heck algebra $H_k(v,t)$.