A discrete branching law for (G,G(ℤ/2ℤ)n)

Let [Formula: see text] be a noncompact simple Lie group, and [Formula: see text] a subgroup of the automorphism group [Formula: see text] for [Formula: see text]. We show a criterion for that there does not exist any infinite dimensional irreducible representation of [Formula: see text] which is algebraically discretely decomposable upon restriction to [Formula: see text]. As an example, we apply the criterion to the split real simple Lie group [Formula: see text] of type [Formula: see text], and verify a conjecture of branching laws for [Formula: see text].