Tetrahedral harmonics revisited

Linear combinations of spherical harmonics are derived that are adapted to the molecular symmetry group T-d(M) and its isomorphic point groups T-d and O. The alternating group T(M), consisting of even permutations, is the semi-direct product V-4(S)C-3, where C-3 = {E, (123), (132)} is a cyclic group and V-4 = {E, (12) (34), (13) (24), (14) (23)}. Further T-d (M) = T(M) (S) {E, (12)*}. This structure of the group enables one to write down simple closed expressions for basis functions. Using the program Maple, tables up to and including l = 10 are generated.