Unitary Irreducible Representations of SU(2, 2). II

Abstract

Paper II of this series [Paper I in J. Math. Phys. 8, 1931 (1967)] is concerned with a general study of the degenerate representations. The explicit expressions for the ``raising'' and ``lowering'' functions ai2(p,q,λ), and bi2(p,q,λ), i = 1, 2, 3, 4 are found. The three Casimir operators C2, C3, and C4 depend on only two complex parameters A and B, a fact reflecting the degenerate nature of the representations under study here. The finite representations are studied first, and thus provide a proof for the degenerate part of Theorem 2, Paper I. The unitary representations are studied next, and we find that there are fourteen classes of degenerate unitary irreducible representations. There are two continuous series, ten discrete series, and two series which depend on one discrete and one continuous parameter. The degenerate part of the D± series is studied, and thus provides an explicit demonstration of Harish-Chandra's theorem.