An L²-cohomology construction of negative spin mass zero equations for U(p, q)

Abstract

In this paper a geometric construction is given of the ladder representations of G = U(p, q) which correspond to negative spin solutions of the massless field equations. The construction is based on the unitary model of the ladder representations in a Bargmann-Segal-Fock space of square-integrable (0, q)-forms. The representations are constructed as holomorphic sections of certain vector bundles over $\text{G}\text{K}$, and the construction is implemented via an integral transform analogous to the Penrose transform of mathematical physics. Finally, the resulting differential equations are exhibited explicitly over $\text{G}\text{K}$.