The Global Dimension of Schur Algebras for GL_2 and GL_3
Representation Theory
2007-05-23 v1 Group Theory
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 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.
Keywords
Cite
@article{arxiv.math/0507521,
title = {The Global Dimension of Schur Algebras for GL_2 and GL_3},
author = {Alison E. Parker},
journal= {arXiv preprint arXiv:math/0507521},
year = {2007}
}
Comments
uses xypic v 3.7 and amsart v. 2.08. 1 figure, 32 pages