Calculate irrep matrices from character tables

[thchr]

An alternative to relying on the irrep matrices from ISOTROPY would be to calculate irrep matrices ourselves from tabulated character tables.

The ingredients necessary to do that are:

• Machine tabulated character tables for all relevant little group irreps. In principle, this should be available among ISOTROPY's datasets. An alternative is to use IrRep's tables which seem to have been derived from Bilbao. There are some issues¹ with that though.

• Implement a method to take a character table and return associated irrep matrices. An algorithm for that is described in Cornwell's Group Theory and Electronic Energy Bands in Solids Chapter 3, §5.3, by using projection operators:

  p. 1	p. 2	p. 3

¹ Unfortunately, IrRep is GNU-v3 licensed and it also seems like they do not actually include all the relevant k-points (e.g., no lines/planes).