Space Groups and Selection Rules

Abstract

A rigorous method is presented for obtaining the Clebsch-Gordan coefficients for the Kronecker products of induced representations of finite groups. The result obtained is applied to the theory of space groups, and the final formula for the coefficients has the advantage, as with other subgroup techniques, of being expressed in terms of the characters of small representations, thereby providing an additional proof independent of Lax, yet supporting his point of view the subgroup and full-group procedures are equivalent, and at the same time the result clarifies subgroup treatments so far given. An example using P23 is given.