A remarkable representation of the SO(3,2) Kac-Moody algebra

We construct a minimal representation of the SO(3,2) Kac-Moody algebra algebra which is based on the spin-zero singleton (the Rac) representation of SO(3,2). The representation is minimal in the sense that the central charge k of the SO(3,2) Kac-Moody algebra is chosen to take the special value of 5/2 which allows the imposition of maximum number of reducibility conditions. For the Rac, this is the unique choice for the remarkable property of maximum reducibility which is consistent with unitarity. To ensure unitarity, we furthermore impose invariance condition under the maximal compact subalgebra SO(3) x SO(2). (author). 19 refs, 1 fig