I like Mulliken notation (A1g, A2g, etc.) for normal point groups as it succinctly represents the symmetry and degeneracy of an irrep within a single symbol. On the other hand, when spin is involved time-reversal symmetry adds complications to the notation. In this spinful double group case, Bethe notation (Gamma1, Gamma2…) is usually used, which is unfortunate since the notation is essentially meaningless and tells you very little.

I have two questions, one which is more general and one for GTPack specifically

- Is there an alternative to Bethe notation in the case of double groups that is more like Mulliken notation? Something like A1g with an overbar to denote (anti)symmetry with respect to time reversal
- Is there any way to get representations with “Mulliken-like” notation for double groups (“SU(2)xS” reps) in the GTCharacterTable and GTSOCSplitting functions?

I agree, Mulliken notation is great. It is not restricted to single-valued groups. See for instance the tables published by Altmann and Herzig (e.g. Ch 14): https://phaidra.univie.ac.at/view/o:104731

Unfortunately, we have not implemented Mulliken notation for double groups yet. However, it is on the ToDo-list.