Neutrino Mixing and the Double Tetrahedral Group

In the spirit of a previous study of the tetrahedral group $T\simeq A_4$, we discuss a minimalist scheme to derive the neutrino mixing matrix using the double tetrahedral group $T^{\mathrm{\prime }}$, the double cover of $T$. The new features are three distinct 2-dimensional representations and complex Clebsch-Gordan coefficients, which can result in a geometric source of CP violation in the neutrino mass matrix. In an appendix, we derive explicitly the relevant group theory for the tetrahedral group $T$ and its double cover $T^{\mathrm{\prime }}$.