SupplementaryMaterial

For each i = 1,...,n, define e i = ei. Lemma 8. Let ρ be an irreducible signed perm-rep. This sequence of inferences holds in the reverse direction as well, and henceρ0 = ψA ρHK as claimed. Proposition 12. Letρ = ρHK;z be an irreducible signed perm-rep. In general,g1 K; however,without loss of generality,assumeg1 = 1so that it is independent ofK.