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We review the deformed W-algebra Wqt(sl_N^) and its screening currents. Weexplicitly construct the local integrals of motion I_n for this deformedW-algebra. We explicitly construct the nonlocal integrals of motion G_n bymeans of the screening currents. Our integrals of motion commute with eachother, and give the elliptic version of those for the Virasoro algebra and theW-algebra W(sl_3^), obtained by V.Bazhanov, A.Hibberd, S.Khoroshkin, S.Lukyanovand Al.Zamolodchikov.

The Integrals of Motion for the Deformed W-Algebra Wqt(sl_N^)