High Quality Content by WIKIPEDIA articles! In mathematics, 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, and have important applications in physics. For example, in case of explicit symmetry breaking, the symmetry group of the problem is reduced from the whole group to one of its subgroup. In quantum mechanics, this reduction in symmetry appears as a splitting of degenerate states into multiplets, as in the Stark or Zeeman effect.