Dimensions of Ext-groups of Weyl modules for GL₂

2013/05/25 by Stephan Baier, Baier, Stephan, Sergey Lamzin +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.NT #math.RT #msc:20G05

paper · pdf · doi:10.48550/arxiv.1305.5947

43 pages, 1 figure, 8 pages of source code of C programs

arxiv created 2013/05/31 · arxiv updated 2013/06/03

Abstract

Let F be an algebraically closed field of positive characteristic p. The third author and Will Turner gave an explicit description of the extension algebra of Weyl modules for GL₂(F). This, in particular, produced an explicit basis. We examine this basis and use it to give upper and lower bounds for the growth behaviour of the dimensions of Ext-groups. Moreover, we implement an algorithm to determine the dimension of any given Ext-group.

Related

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• On the good filtration dimension of Weyl modules for a linear algebraic group
• Bounds on the Dimension of Ext for Finite Groups of Lie Type
• The Weyl extension algebra of GL₂(\mathbbF_p)
• Dimensions of Higher Extensions for SL₂