  We have developed a Mathematica program package SpaceGroupIrep which is a
database and tool set for irreducible representations (IRs) of space group in
BC convention, i.e. the convention used in the famous book "The mathematical
theory of symmetry in solids" by C. J. Bradley & A. P. Cracknell. Using this
package, elements of any space group, little group, Herring little group, or
central extension of little co-group can be easily obtained. This package can
give not only little-group (LG) IRs for any k-point but also space-group (SG)
IRs for any k-stars in intuitive table form, and both single-valued and
double-valued IRs are supported. This package can calculate the decomposition
of the direct product of SG IRs for any two k-stars. This package can determine
the LG IRs of Bloch states in energy bands in BC convention and this works for
any input primitive cell thanks to its ability to convert any input cell to a
cell in BC convention. This package can also provide the correspondence of
k-points and LG IR labels between BCS (Bilbao Crystallographic Server) and BC
conventions. In a word, the package SpaceGroupIrep is very useful for both
study and research, e.g. for analyzing band topology or determining selection
rules.
