### 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 |
---|---|

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

*Journal of Algebra*,

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

**The weighted fusion category algebra and the q-Schur algebra for GL(2)(q).** / Park, Sejong.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 319, no. 1, pp. 93-101. https://doi.org/10.1016/j.jalgebra.2007.10.025

}

TY - JOUR

T1 - The weighted fusion category algebra and the q-Schur algebra for GL(2)(q)

AU - Park, Sejong

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

AB - 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.

KW - function system

KW - weighted fusion category algebra

KW - Alperin's weight conjecture

KW - q-Schur algebra

KW - general linear-groups

U2 - 10.1016/j.jalgebra.2007.10.025

DO - 10.1016/j.jalgebra.2007.10.025

M3 - Article

VL - 319

SP - 93

EP - 101

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -