Crystallographic viewpoints in the classification of space-group representations

Abstract

Abstract The available tables of irreducible representations of space groups differ considerably in completeness, kind of listing, and nomenclature. Although published more than 50 years ago, Wintgen's approach making use of the isomorphism between the reciprocal-space groups and the symmorphic space groups has not yet been applied in any of the published listings of irreducible representations of the space groups. In this paper the implications of such a classification scheme are discussed. Use of the International Tables for Crystallography, Vol. A makes such a classification simpler, more transparent, and facilitates some applications. Moreover, the International Tables may serve as a basis for the standardization of the types and symbols of representations.