On the characters of the Weyl group of type C

Abstract

We continue our study of the characters of the Weyl groups of the simple Lie algebras, begun in [2], in order to find a unified theory using their common structure as reflection groups. Carter [1] dealt with the same problem for the conjugacy classes, and we will adopt his use of Weyl subgroups. In this paper we look at the Weyl group of type C or hyper-octahedral group—the wreath product C 2 ≀ S l . We first construct the irreducible characters from those of the symmetric group and, like the conjugacy classes, they will be parameterized by pairs of partitions. We shall then be able to give an algorithm generalizing the partial ordering on partitions given in [2], which will allow us to determine the irreducible constituents of the principal character of a Weyl subgroup induced up to the whole group.