Does anyone know who started using the symbols A, B, E, T (First column, left) for showing irreducible representations of symmetry groups? In older maths books I see capital gamma. Herein A= totally symmetric, B= anti-symmetric with respect to rotation, E= doubly degenerate, T is triply degenerate irreducible representation. The symbols in the top row are due to Schonflies (D4h, C, S, Sigma).
Many books/ webpages claim that Mulliken started this symbols, and they are indeed called Mulliken symbols http://www.cup.uni-muenchen.de/ch/compchem/geom/point3.html, however, many other physicists were using A, B, E and T symbolism at the same time (1930s). The letter C was not used. It appears that mathematicians must be using these symbols before that but I could not find any example. Is anyone aware of the history of character tables such as the one shown here? Thank you.