×

Specht modules for Weyl groups. (English) Zbl 0820.20013

Over fields of characteristic zero, there are well known constructions of the irreducible representations and of irreducible modules, called Specht modules for the symmetric groups \(S_ n\) which are based on elegant combinatorial concepts connected with Young tableaux etc. James extended these ideas to construct irreducible representations and modules over arbitrary fields. E. Al-Aamily, A. O. Morris and M. H. Peel [J. Algebra 68, 298-305 (1981; Zbl 0463.20009)] showed how this construction could be extended to deal with the Weyl groups of type \(B_ n\). [In Astérisque 87/88, 267-287 (1981; Zbl 0492.20008)] the second author described a possible extension of James’s work for Weyl groups in general, where Young tableaux are interpreted in terms of root systems. We now modify these results and give an alternative generalisation of James’s work which is an improvement and extension of the original approach suggested by Morris.

MSC:

20C30 Representations of finite symmetric groups
20F55 Reflection and Coxeter groups (group-theoretic aspects)
05E10 Combinatorial aspects of representation theory
PDFBibTeX XMLCite
Full Text: arXiv EuDML EMIS