Seminar on low-dimensional mathematics March 16, 2007 Takeo Kojima (Tokyo) The Integrals of Motion for the Deformed W-algebra We review the deformed W-algebra Wq,t(sl_N^), which is the elliptic version of the W-algebra W(sl_N^). By means of this deformed W-algebra, we explicitly construct two classes of infinitly many commutative operators : Local Integrals of Motion I_n and Nonlocal Integrals of Motion G_n. The Local Integrals of Motion I_n give elliptic-quantization of the conservation laws of KP-hierarchy. The Nonlocal Integrals of Motion G_n give elliptic-quantization of the Hamiltonians of the affine-Toda. The Integrals of Motions I_n and G_n commute with each others: [I_n, I_m]=[G_n, G_m]=[I_n, G_m]=0, (m,n=1,2,3,...). This work is collaboration with B.Feigin, J.Shiraishi and H.Watanabe. --- http://www.pdmi.ras.ru/~lowdimma