Clebsch–Gordan coefficients for the group chains O ⊃ T ⊃ D2 and Td ⊃ T ⊃D2 by the method of projective representations

The spinor representations for the groups forming the chains O ? T ? D ₂ and T _d ? T ? D ₂ are constructed as projective representations. The Clebsch–Gordan coefficients are then calculated using a standard method. Projective factor systems, irreducible representations, canonical bases, and tables of Clebsch–Gordan coefficients are given. The subduction from O to D ₃ is discussed.