Modified group projector technique: Induced representations

Abstract

The group projector technique is developed for the representations of the direct product form, D=D'(X)d, in which one of them has been induced from a representation of a subgroup. It is shown that the group projectors and symmetry-adapted bases are essentially determined in terms of the subgroup representations. To illustrate both the technical and conceptual advantages of the method, it is shown how the calculation of the normal modes of polymers (polyacetylene as an example) can be obtained using the symmetry of the monomer only, and several results of the induction theory are reconsidered within the new framework.