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arXiv:math/0507521 [math.RT]AbstractReferencesReviewsResources

The Global Dimension of Schur Algebras for GL_2 and GL_3

Alison E. Parker

Published 2005-07-26Version 1

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.

Comments: uses xypic v 3.7 and amsart v. 2.08. 1 figure, 32 pages
Journal: J. Algebra, 241 (2001), 340-378
Categories: math.RT, math.GR
Subjects: 16G99, 20G05, 20G10, 20G42
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