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Permutation representations and a fragment of the decomposition matrix of symplectic and special linear groups over a finite field. (English. Russian original) Zbl 0761.20018

Sib. Math. J. 31, No. 5, 744-755 (1990); translation from Sib. Mat. Zh. 31, No. 5(183), 46-60 (1990).
Given a prime \(p\) and \(q=p^ d\), an explicit construction of a fragment of the decomposition matrix of the groups \(SL_ n(q)\) and \(Sp_ n(q)\) is given for any \(n\). The basic method is the analysis of the modular permutation representation over an algebraically closed field of characteristic \(p\). At the same time, composition factors of this representation with their multiplicities are described.
Reviewer: Z.Vavrin (Praha)

MSC:

20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
20C20 Modular representations and characters
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References:

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