[GAP Forum] Calculation and derivation the small representations of little groups and the corepresentations of magnetic space groups systematically.

[Hongyi Zhao]

Hi GAP team,

The following two group theory representations are the core and
foundation of the application of group theory in the fields of
crystallography, solid state physics and quantum mechanics:

1. The small representations of little groups, as described in the BC
book section 4.4 "The small representations of little groups".
2. The corepresentations of magnetic space groups, as described in the
BC book chapter 7 "The magnetic groups and their corepresentations".

Nevertheless, the corresponding theories are quite complicated, and
the resulting data is very diverse. Without the help of the computer,
it is difficult to remember and infer the corresponding
representations, and it is impossible to correctly analyze the
relationship between them.

So, I wonder if GAP can be used to build these databases systematically.

For your reference, see here [1] for the BC book mentioned here.

[1] https://github.com/hongyi-zhao/ebooks/blob/master/The-Mathematical-Theory-of-Symmetry-in-Solids.pdf

Yours sincerely,
-- 
Assoc. Prof. Hongsheng Zhao <hongyi.zhao at gmail.com>
Theory and Simulation of Materials
Hebei Vocational University of Technology and Engineering
No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province