2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75895We first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL_2 and SL_3. We use these to show that the global dimension of a Schur algebra for GL_2 and GL_3 is twice the good filtration dimension. To do this for SL_3, we give an explicit filtration of the modules \nabla(λ) by modules of the form \nabla(μ)^F \otimes L(ν) where μis a dominant weight and νis p-restricted.uses xypic v 3.7 and amsart v. 2.08. 1 figure, 32 pagesRepresentation TheoryGroup Theory16G99, 20G05, 20G10, 20G42text