Plethysm and the Theory of Complex Spectra

Notable progress in developing the theory of complex spectra has come from the exploitation of the symmetry properties of atomic wavefunctions using the theory of continuous groups. Many seemingly simple results have previously been obtained by what would appear to be unreasonably complex methods. Many of these complexities may be removed, and new results derived, using the algebra of plethysm first developed by Littlewood. Applications to three central problems in the theory of complex spectra are discussed: (1) the classification of the atomic states of n-electron configurations; (2) the analysis and classification of the N-particle operators that arise in the application of perturbation theory to atomic problems; (3) the derivation of selection rules for the matrix elements of operators.