Enumeration of Group Invariant Quartic Polynomials in Higgs Scalar Fields

Abstract

The. properties of Schur functions are used to enumerate the terms that must appear in a G-invariant symmetric quartic polynomial constructed from a set of Higgs fields. The importance of classifying Higgs fields as to their orthogonal, symplectic or complex representations is emphasized. The peculiar difficulties associated with symplectic irreps are noted. The groups SUs and SOlO are used to provide examples of the methods developed.