Application of coset representations to the construction of symmetry adapted functions

Abstract

A coset representation (G(/Gi)), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupGi, is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/Gi) orbit belongs to theGi site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.