IRREDUCIBILITY OF LADDER REPRESENTATIONS OF U(2,2) WHEN RESTRICTED TO POINCARE SUBGROUP

It is shown that the most degenerate discrete series of unitary irreducible representations of U(2, 2), the so-called ladder representations, remain irreducible when restricted to representations of the Poincaré subgroup ISL(2, C). They correspond to representations of this subgroup with mass zero and arbitrary integer or half-integer helicity λ. The basis vectors of the canonical basis are calculated as functions of a lightlike 4-vector, which is formed by the simultaneous eigenvalues of the generators of the subgroup of translations.