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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the decomposition numbers of the finite general linear groups. II

Author: Richard Dipper
Journal: Trans. Amer. Math. Soc. 292 (1985), 123-133
MSC: Primary 20C20; Secondary 20G40
MathSciNet review: 805956
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Abstract: Let $ q$ be a prime power, $ G = {\operatorname{GL} _n}(q)$ and let $ r$ be a prime not dividing $ q$. Using representations of Hecke algebras associated with symmetric groups over arbitrary fields, the $ r$-modular irreducible $ G$-modules are classified. The decomposition matrix $ D$ of $ G$ (with respect to $ r$) is partly described in terms of decomposition matrices of Hecke algebras, and it is shown that $ D$ is lower unitriangular, provided the irreducible characters and irreducible Brauer characters of $ G$ are suitably ordered.

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Article copyright: © Copyright 1985 American Mathematical Society