Molien function and calculation of invariant polynomials for space groups

Abstract

We have developed an algorithm for the computation of the Molien function (generating for the multiplicity of the identity representation in the symmetrized n^th power of representation P of group G) and used it to compute the Molien function for irreducible representations of crystal space groups. The calculation is illustrated upon some irreducible representations of the crystal space groups. Ir. particular, a case of interest is some irreducible representations of the crystal space group 0 ³_h -Pn3m. Quartic invariants are exhibited for irreducible representations *X (j) and *R (j)j= 1,2,3,4 of 0 O ³_h .