Branching rules for the Weyl group orbits of the Lie algebra An

The orbits of Weyl groups W(An) of simple An-type Lie algebras are reduced to the union of orbits of the Weyl groups of maximal reductive subalgebras of An. Matrices transforming points of the orbits of W(An) into points of subalgebra orbits are listed for all cases n ≤ 8 and for the infinite series of algebra-subalgebra pairs An contains An-k-1 x Ak x U1, A2n contains Bn, A2n-1 contains Cn, A2n-1 contains Dn. Numerous special cases and examples are shown.