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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the decomposition numbers of the finite general linear groups. II
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by Richard Dipper PDF
Trans. Amer. Math. Soc. 292 (1985), 123-133 Request permission

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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • 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