LAUSR

Clifford algebras $$C \ell _{2,0}$$Cℓ2,0 and $$C \ell _{1,1}$$Cℓ1,1 are isomorphic simple algebras whose Salingaros vee groups belong to a class $$N_1$$N1. The algebras are isomorphic to the quotient algebra $$\mathbb {R}[D_8]/\mathcal {J}$$R[D8]/J of the group algebra of the dihedral group $$D_8$$D8 modulo an ideal $$\mathcal {J}=(1+\tau )$$J=(1+τ) where $$\tau $$τ is a central involution in $$D_8$$D8. Since all irreducible characters of $$D_8$$D8, including a single nonlinear character of degree 2, can be realized over $$\mathbb {R}$$R, spinor representations of the Clifford algebras can be realized over $$\mathbb {R}$$R and so $$C \ell _{2,0} \cong C \ell _{1,1} \cong \mathbb {R}(2)$$Cℓ2,0≅Cℓ1,1≅R(2). Spinor modules in $$C \ell _{2,0}$$Cℓ2,0 and $$C \ell _{1,1}$$Cℓ1,1 are isomorphic to irreducible $$\mathbb {R}D_8$$RD8-submodules of dimension 2 of the regular module $$\mathbb {R}D_8$$RD8. As such, they are uniquely determined by the nonlinear character of degree 2. These results are generalized to the vee groups in classes $$N_{2k-1}$$N2k-1 and $$\Omega _{2k-1}$$Ω2k-1 ($$1 \le k \le 4$$1≤k≤4). It is proven that each irreducible character of $$G_{p,q}$$Gp,q in these classes can be realized over $$\mathbb {R}.$$R. Consequently, every nonlinear character of $$G_{p,q}$$Gp,q uniquely determines a spinor module of $$C \ell _{p,q}$$Cℓp,q which is faithful (resp. unfaithful) when $$G_{p,q}$$Gp,q is in the class $$N_{2k-1}$$N2k-1 (resp. $$\Omega _{2k-1})$$Ω2k-1). This paper is a continuation of [1].