Structure and representations of the symmetry group of the four-dimensional cube

Abstract

In this paper we give, explicitly, the description of the structure, the characters, and the complete system of irreducible representations of the hyperoctahedral group in four dimensions, which we call W4 (from the German ’’Würfel’’). In a second step, we do the same for the subgroup SW4, which is formed by all pure rotations contained in W4.