The projective representations of the hyperoctahedral group

Abstract

The hyperoctahedral group (the Weyl group of the root system Bn) has seven distinct nonsplit double covers (for n [ges] 4), and hence, seven families of projective representations. We give constructions of all the irreducible representations of these seven double covers in terms of symmetric group representations, and determine the associated character tables. As a corollary, we also obtain the irreducible projective representations and characters of the Weyl group of the root system Dn.