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