Application of the Band Representations of Space Groups in the Theory of Electronic States of Crystalline Solids. I. General Consideration of the Band Representations

Band representations are considered in the framework of the ordinary representation theory of space groups. The band representation characterizes the symmetry of all the electronic states of an energy band. Any band representation coincides with a so‐called simple band representation or is a direct sum of the latter. The whole number of simple band representations is finite for any space group. The type of a band representation determines the symmetry of the localized functions related with a given energy band.