Specht Modules for Weyl Groups

Abstract

Over fields of characteristic zero, there are well known construction 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.(see, e.g.[10]). James [8] extended these ideas to construct irreducible representations and modules over arbitrary field. Al-Aamily, Morris and Peel [ 1 ] showed how this construction could be extended to deal with the Weyl groups of type $B_{n}$. In [11] the second author described a possible extension of James' 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' work which is an improvement and extension of the original approach suggested by Morris.