Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups

TLDR

The Bilbao Crystallographic Server is a free online portal offering crystallographic programs and databases, providing access to symmetry group data, subgroups, Brillouin zones, and related tools. This article presents tools for constructing irreducible representations of point and space groups, analyzing group‑subgroup representation correlations, and decomposing Kronecker products.

Abstract

The Bilbao Crystallographic Server is a web site with crystallographic programs and databases freely available on-line (http://www.cryst.ehu.es). The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones etc.). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group-subgroup relations between space groups (subgroups and supergroups, Wyckoff-position splitting schemes etc.). There are also software packages studying specific problems of solid-state physics, structural chemistry and crystallography. This article reports on the programs treating representations of point and space groups. There are tools for the construction of irreducible representations, for the study of the correlations between representations of group-subgroup pairs of space groups and for the decompositions of Kronecker products of representations.