2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128401We review the deformed W-algebra Wqt(sl_N^) and its screening currents. We explicitly construct the local integrals of motion I_n for this deformed W-algebra. We explicitly construct the nonlocal integrals of motion G_n by means of the screening currents. Our integrals of motion commute with each other, and give the elliptic version of those for the Virasoro algebra and the W-algebra W(sl_3^), obtained by V.Bazhanov, A.Hibberd, S.Khoroshkin, S.Lukyanov and Al.Zamolodchikov.Proceedings for Representation Theory 2006, Atami, Japan, p.102-114, (2006), [ISBN4-9902328-2-8]Mathematical Physics81B68, 17B68text