Symbolic Algorithm for Generating Irreducible Bases of Point Groups in the Space of SO(3) Group

Abstract

A symbolic algorithm which can be implemented in computer algebra systems for generating bases for irreducible representations of the laboratory and intrinsic point symmetry groups acting in the rotor space is presented. The method of generalized projection operators is used. First the generalized projection operators for the intrinsic group acting in the space $\mathrm{L}^2{\textrm{SO3}}$ are constructed. The efficiency of the algorithm is investigated by calculating the bases for both laboratory and intrinsic octahedral groups irreducible representations for the set of angular momenta up to J=10.