Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20C20, 20G40

Retrieve articles in all journals with MSC: 20C20, 20G40

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society