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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
DOI: https://doi.org/10.1090/S0002-9947-1985-0805956-7
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