Abstract
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 SL2 and SL3. We use these to show that the global dimension of a Schur algebra for GL2 and GL3 is twice the good filtration dimension. To do this for SL3, we give an explicit filtration of the modules ∇(λ) by modules of the form ∇(μ)F⊗L(ν) where μ is a dominant weight and ν is p-restricted.
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