Branching of representations to symmetric subgroups

Let g be the Lie algebra of a compact Lie group and let θ be any automorphism of g. Let k denote the fixed point subalgebra g . In this paper we present LiE programs that, for any finite dimensional complex representation π of g, give the explicit branching π|k of π on k. Cases of special interest include the cases where θ has order 2 (corresponding to compact Riemannian symmetric spaces G/K), where θ has order 3 (corresponding to compact nearly-Kaehler homogeneous spaces G/K), where θ has order 5 (which include the fascinating 5-symmetric space E8/A4A4), and the cases where k is the centralizer of a toral subalgebra of g.