Computation of irreducible decompositions of permutation representations of wreath products of finite groups

An algorithm for the computation of the complete set of primitive orthogonal idempotents of the centralizer ring of the permutation representation of the wreath product of finite groups is described. This set determines the decomposition of the representation into irreducible components. In the quantum mechanics formalism, the primitive idempotents are projection operators onto irreducible invariant subspaces of the Hilbert space describing the states of many-particle quantum systems. The proposed algorithm uses methods of computer algebra and computational group theory. The C implementation of this algorithm is able to construct decompositions of representations of high dimensions and ranks into irreducible components.