MATRIX UNITS FOR THE GROUP ALGEBRA kG(f) = k((Z(2) x Z(2)) (sic) S-f)

The irreducible representations of the group Gf := (Z(2) x Z(2)) vertical bar Sf are indexed by 4-partitions of f, i.e., by the set {[alpha] (3)[beta] (2)[gamma] (1)[delta] (0) |alpha proves u(3), beta proves u(2),. gamma proves u(1), delta proves u(0), u(0) + u(1)+ u(2)+ u(3) = f}. This set is in 1 - 1 correspondence with partitions of 4f whose 4-core is empty. In this paper we construct the inequivalent irreducible representations of Gf. We also compute a complete set of seminormal matrix units for the group algebra kGf.