  The orbits of Weyl groups W(A(n)) of simple A(n) type Lie algebras are
reduced to the union of orbits of the Weyl groups of maximal reductive
subalgebras of A(n). 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 A(n) - A(n-k-1) x A(k) x U(1), A(2n) - B(n),
A(2n-1) - C(n), A(2n-1) - D(n). Numerous special cases and examples are shown.
