2003/12/04 by S. Halicioğlu
Mathematics · #math.RT #msc:20C15 #msc:20C30
published as Glasgow Math. J. 37 (1995), no. 3, 279--287
arxiv created 2003/12/04 · arxiv updated 2009/12/01
Over fields of characteristic zero, there are well known constructions of the irreducible representations, due to A Young, and of irreducible modules, called Specht modules, due to W Specht, for the symmetric groups Sn which are based on elegant combinatorial concepts connected with Young tableaux etc.(see, e.g.\bf [13]). James \bf [12] extended these ideas to construct irreducible representations and modules over arbitrary field. Al-Aamily, Morris and Peel \bf [1] showed how this construction could be extended cover the Weyl groups of type Bn. In \bf [14] Morris described a possible extension of James' work for Weyl groups in general. Later, the present author and Morris \bf [8] give an alternative generalisation of James' work which is an extended improvement and extension of the original approach suggested by Morris. We now give a possible extension of James' work for finite reflection groups in general.