The authors describe the linear T ⊗ τ₂ Jahn-Teller interaction as a pseudoscalar operator in electron-phonon space. In this form it is found to mix states within an invariant minimal subspace for which they give basis vectors in an analytic form for arbitrary phonon numbers. These vibronic states are labelled by spherical symmetry quantum numbers and possess definite cubic symmetry at the same time. It is shown how to extend the method to the case when the Jahn-Teller interaction competes with spin-orbit coupling.