Unitary Irreducible Representations of the Groups SO(n, 1)

By SO0(n, 1) we denote the identity component of the group O(n, 1), by so(n, 1), the Lie algebra of SO0(n, 1). We determine all those representations of the Lie algebras so(n, 1) which can be extended to a unitary irreducible representation of the group and give explicit expressions for the generators. The general results are specialized to the cases n = 2, 3, 4, and 5.