Selection rule for transitions between electron states in solids

Space-group theory, which is a mathematical device to describe symmetry properties in crystals, has been employed successfully to solve a broad range of problems in solid-state physics and chemistry. The determination of selection rules is formulated in group-theory language as an expansion of the direct product of irreducible representations that transform the wave functions of the initial and final states. This paper proposes a method of determining the selection rules based on the theory of induced representations and derives an algorithm that makes use only of representations of the group of the wave vector k, complete tables of which are available.