  We 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(\lambda) by modules of the form \nabla(\mu)^F \otimes
L(\nu) where \mu is a dominant weight and \nu is p-restricted.
