Branching rules for Weyl group orbits involving the Lie algebra U(1)

The orbits of Weyl groups W(L) of all simple Lie algebras L are reduced to the union of orbits of the Weyl groups of maximal reductive non-semisimple subalgebras L' of L, whenever such subalgebras are present. Matrices transforming points of the orbits of W(L) into points of W(L') orbits are listed for the infinite series of algebra-subalgebra pairs An superset of An-k-1 x Ak x U(1), Bn superset of An-1 x U(1), Dn superset of An-1 x U(1), Dn superset of Dn-1 x U(1), Dn superset of Dn-1 x U(1), and for E6 superset of E5 x U(1) and E7 superset of E6 x U(1). Examples of branching rules are shown for all cases.