The evaluation of branching rules for linear groups using mappings between weight spaces

Abstract

Consideration of the branching rules associated with the embedding of L(h) in L(g) leads to a method for the determination of the related plethysms { λ } ⊗ { μ }. The embedding is defined by the correspondence between the basis states of the representations { 1 } and { λ } of L( g) and L(h). These basis states are specified by weights, and the branching rules are determined by carrying out mappings between the weight spaces of the groups. Maximum use is made of the Weyl symmetry to establish an algorithm which has been used to calculate a large number of plethysms