The weighted fusion category algebra and the qSchur algebra for \mathrm{GL}_2(q)
Abstract
We show that the weighted fusion category algebra of the principal 2block $b_0$ of $\mathrm{GL}_2(q)$ is the quotient of the $q$Schur algebra $\mathcal{S}_2(q)$ by its socle, for $q$ an odd prime power. As a consequence, we get a canonical bijection between the set of isomorphism classes of simple $k\mathrm{GL}_2(q)b_0$modules and the set of conjugacy classes of $b_0$weights in this case.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1622
 Bibcode:
 2007arXiv0711.1622P
 Keywords:

 Mathematics  Representation Theory;
 20C20;
 20J05
 EPrint:
 8 pages, 2 figures, to appear in Journal of Algebra