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

Sejong Park

doi:10.1016/j.jalgebra.2007.10.025

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

Sejong Park

Mathematical Science

Research output: Contribution to journal › Article

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	https://doi.org/10.1016/j.jalgebra.2007.10.025
Publication status	Published - 1 Jan 2008

Keywords

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

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10.1016/j.jalgebra.2007.10.025

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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.",

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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 -

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

Abstract

Keywords

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