The Global Dimension of Schur Algebras for GL2 and GL3

✍ Scribed by Alison E Parker

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 255 KB
• Volume: 241
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8759

✦ Synopsis

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 and SL . We use these to show that the global 2 3 dimension of a Schur algebra for GL and GL is twice the good filtration 2 3

Ž . dimension. To do this for SL , we give an explicit filtration of the modules ٌ by 3 Ž . F Ž . modules of the form ٌ m L where is a dominant weight and is p-restricted.