  The property of some finite W-algebras to appear as the commutant of a
particular subalgebra in a simple Lie algebra G is exploited for the obtention
of new G-realizations from a "canonical" differential one.
  The method is applied to the conformal algebra so(4,2) and therefore yields
also results for its Poincare subalgebra. Unitary irreducible representations
of these algebras are recognized in this approach, which is naturally compared
-or associated- to the induced representation technic.
