2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130925The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra gl(n). For the special case of simple modules we naturally deduce a categorification via modules over the cohomology ring of certain flag varieties. Further geometric categorifications and the relation to Steinberg varieties are discussed. We also give a categorical version of the quantised Schur-Weyl duality and an interpretation of the (dual) canonical bases and the (dual) standard bases in terms of projective, tilting, standard and simple Harish-Chandra bimodules.Quantum AlgebraRepresentation Theory20G42, 17B10, 14M15, 16G10text