The Global Dimension of Schur Algebras for GL_2 and GL_3
Abstract
Description
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(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 pages
uses xypic v 3.7 and amsart v. 2.08. 1 figure, 32 pages