2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61976We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n, and give a complete reducibility result. These quantum groups have a natural n-dimensional module V. We prove an analogue of Schur-Weyl duality in this setting: the centralizer algebra of the quantum group action on the k-fold tensor power of V is a quotient of a Hecke algebra for all n and is isomorphic to the Hecke algebra in case n\geq k.25 pages, AMS-TeXQuantum AlgebraRepresentation Theory17B37, 16W30, 16W35, 81R50text