Kronecker products for compact semisimple Lie groups

Abstract

A review is given of the application of S-function techniques to the evaluation of Kronecker products of irreducible representations of compact semisimple Lie groups. Explicit formulae are derived for all irreducible representations of all such groups. Recent developments involving composite Young diagrams are brought to fruition and the vexed problem of SO_2k is dealt with completely. New branching rules for the classical groups are given in an appendix. These are exploited in the evaluation of Kronecker products by means of a technique which is applied to both classical and exceptional groups. A discussion is made of various modification rules which are needed to express the final results in standard form.