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.

up vote 2 down vote accepted

Mulliken credits Georg Placzek in his autobiography (1989, p. 90). According to T. Oka (2011)(pdf):

Placzek (1934) introduced the currently used symbols of irreducible representations such as A (symmetric), B (antisymmetric), E (“entartet”, doubly degenerate), F (triply degenerate), subscript 1 and 2 (to specify symmetry with respect to C2) and superscript ′ and ′′ (to specify symmetry with respect to σ), etc. While a little unsystematic, the much-needed nomenclature was immediately adopted by theorists like Teller, Tisza, Mulliken, Wilson, and others, and has become the fixture in molecular spectroscopy.


Placzek, G. (1934) Rayleigh-Streuung und Raman-effekt. Marx’s Handbuch der Radiologie, VI, (Part II), 209–374.

  • Thank you very much. Glad to know that he mentioned that in his autobiography. – M. Farooq Aug 1 at 3:05

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