  Let g be a semisimple Lie algebra over the real numbers. We describe an
explicit combinatorial construction of the real Weyl group of g with respect to
a given Cartan subalgebra. An efficient computation of this Weyl group is
important for the classification of regular semisimple subalgebras, real
carrier algebras, and real nilpotent orbits associated with g; the latter have
various applications in theoretical physics.
