Discrete Series for the Universal Covering Group of the 3 + 2 de Sitter Group

Abstract

A classification is given of the irreducible unitary representations of the universal covering group of the 3 + 2 de Sitter group which contract to the usual physical representations of the Poincaré group. These representations include the discrete series for the 3 + 2 de Sitter group. The classification problem is reduced from one for the group to the corresponding one for the Lie algebra. The method used by Thomas for the representations of the 4 + 1 de Sitter group is then followed, except that a representation is reduced out with respect to the irreducible unitary representations of a noncompact 2 + 2 subalgebra. It is conjectured that each representation of this subalgebra occurs at most once. The action on the representation spaces of a basis for the Lie algebra is given. The contractions of the representations to those of the Poincaré, oscillator and the Galilei groups are briefly considered.