### Abstract

We show that the weighted fusion category algebra of the principal 2-block b(0) of GL(2)(q) is the quotient of the q-Schur algebra 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 kGL(2) (q)b(0)-modules and the set of conjugacy classes of b(0)-weights in this case. (C) 2007 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 93-101 |

Number of pages | 9 |

Journal | Journal of Algebra |

Volume | 319 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2008 |

### Keywords

- function system
- weighted fusion category algebra
- Alperin's weight conjecture
- q-Schur algebra
- general linear-groups

## Cite this

Park, S. (2008). The weighted fusion category algebra and the q-Schur algebra for GL(2)(q).

*Journal of Algebra*,*319*(1), 93-101. https://doi.org/10.1016/j.jalgebra.2007.10.025