The weighted fusion category algebra and the q-Schur algebra for \mathrm{GL}_2(q)

Details The weighted fusion category algebra and the q-Schur algebra for \mathrm{GL}_2(q) The weighted fusion category algebra and the q-Schur algebra for \mathrm{GL}_2(q)

2007-11-10

arxiv.org/abs/0711.1622v1

Mathematics

Representation Theory

8 pages, 2 figures, to appear in Journal of Algebra

Scientific paper

We show that the weighted fusion category algebra of the principal 2-block $b_0$ 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.

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