Computing the real Weyl group

Let g be a semisimple Lie algebra over the field of real numbers. G group with g. The Weyl respect to Cartan subalgebra h is defined as W(G,h)=NG(h)/ZG(h). We describe an explicit construction W(G,h) for groups that arise set points connected algebraic groups. show this also gives when adjoint This algorithm important classification regular subalgebras, carrier algebras, and nilpotent orbits associated g; latter have various applications in theoretical physics.