Relationship of the Internal and External Multiplicity Structure of Compact Simple Lie Groups

As a preliminary step in a program aimed at developing the Racah algebra of an arbitrary compact simple Lie group L, this paper gives a unified review with various extensions of the work of Biedenharn, Speiser, and others on the relationship between the internal and external multiplicity structures of L, the former being that of the weights of the representations of L, the latter being that of the terms of the Clebsch-Gordan series of L.