ABSTRACT
This chapter begins by reviewing some standard definitions and results on finite reflection groups. It is devoted to the study of a particular series of finite reflection groups: the hyperoctahedral groups. The chapter describes a large class of representations associated to the hyperoctahedral groups. Bifurcation theory on these representations has a rich and varied structure. The chapter reviews the definition of wreath product and then describes a class of examples which is closely related to wreath product subgroups of the hyperoctahedral groups. It concludes with some examples of wreath products where the ‘internal’ symmetry group is a finite reflection group.
