Application of Band Representations of Space Groups in the Theory of Phase Transitions and Point Defects in Crystals

Abstract It is shown that simple band representations tables can be used to solve the following two problems: 1) to find the irreducible components of the space group representations induced by the irreducible representations of their site symmetry subgroups; 2) to find the irreducible components of the site symmetry group representations subduced by irreducible representations of a space group. The solution of both the problems requires also the induced representation table for the crystallographic point grousp which is given here. The space group D is considered as an example. The simple band representations table for this group is also given. The application of the band representations of space groups in the theory of second‐order phase transitions and in the theory of point defects in crystals is discussed.