Kronecker Products and Symmetrized Squares of Irreducible Representations of Space Groups

Application is made to space groups of a theorem by Mackey on the symmetrized and antisymmetrized squares of induced representations. A new and constructive proof is given of Mackey's theorem which enables the representations appearing in the decomposition of the symmetrized squares to be easily identified. The method is used to extend Birman's tables for Td2, the zinc-blende structure, to include products involving its double-valued representations