Use this tag for questions about rules for decomposing the restriction of an irreducible representation of a group into irreducible representations of a subgroup.
Restriction is a fundamental construction in representation theory of groups. Restriction forms a representation of a subgroup from a representation of the whole group. Often the restricted representation is simpler to understand. Rules for decomposing the restriction of an irreducible representation into irreducible representations of the subgroup are called branching rules.
Classical branching rules describe the restriction of an irreducible representation (π, V) of a classical group to a classical subgroup H, i.e., the multiplicity with which an irreducible representation (σ, W) of H occurs in π. By Frobenius reciprocity for compact groups, that is equivalent to finding the multiplicity of π in the unitary representation induced from σ.
