A new verification of Kovalev's tables of irreducible representations of the space groups

In the application of representation theory to physical and crystallographic problems, Kovalev's tables provide a uniquely reliable and complete source for the required irreducible representations of the space groups. A number of programs based on these tables, designed to automate the lengthy calculations involved, generate non-physical or incorrect solutions to some problems, raising questions over the validity of Kovalev's work. In this work the tables are verified to the point of homomorphism with the groups and subgroups that they represent through the use of the digitized versions of the tables used in SARAh. The results support the correctness of Kovalev's definitions, highlighting difficulties in interpreting the tables themselves and some general failings of the programs used in the application of representation theory to physical problems.