Canonical forms of tensor representations and spontaneous symmetry breaking

Abstract

An algorithm for constructing canonical forms for any tensor representation of the classical compact Lie groups is given. This method is used to find a complete list of the symmetry breaking patterns produced by Higgs fields in the third-rank antisymmetric representations of U(n), SU(n) and SO(n) for n<or=7. A simple canonical form is also given for kth-rank symmetric tensor representations.