A characterization of "Heisenberg groups"; when is a particle free?
Larry Baggett · Rocky Mountain Journal of Mathematics · 1978
Let H be a connected Lie subgroup of a connected Lie group G. Sufficient conditions are given to ensure that the smallest closed normal subgroup of G containing H is a generalized Heisenberg group.The conditions are that there should exist an irreducible representation T of G and a nonzero vector \(T h (T g (<p)), T g (