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A computer oriented algorithm for the determination of the dimension and character of a modular irreducible SL(n,K)-module. (English) Zbl 0678.20024

Let k be an infinite field of characteristic p. For the case \(p=0\), H. Weyl gave explicit formulae for the dimensions and characters of irreducible SL(n,k)-modules. For \(p>0\), this is an open (and important) problem in the representation theory of algebraic groups. In this paper, the authors give an algorithm towards the computation of the dimensions and characters of the modular, rational irreducible representations of SL(n,k), for \(p>0\). This paper is an important contribution to the representation theory of algebraic groups.
Reviewer: V.Lakshmibai

MSC:

20G05 Representation theory for linear algebraic groups
20C20 Modular representations and characters
20-04 Software, source code, etc. for problems pertaining to group theory
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References:

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