Computing the real Weyl group. (May 2021) - Dietrich, Heiko; de Graaf, Willem A.
Abstract: Let g be a semisimple Lie algebra over the field of real numbers. Let G be a real Lie group with Lie algebra g . The real Weyl group of G with respect to a Cartan subalgebra h of g is defined as W ( G, h ) = N G ( h ) / Z G ( h ) . We describe an explicit construction of W ( G, h ) for Lie groups G that arise as the set of real points of connected algebraic groups. We show that this also gives a construction of W ( G, h ) when G is the adjoint group of g . This algorithm 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.