Group-Theoretical Approach to Extended Conformal Supersymmetry: Function Space Realizations and Invariant Differential Operators

Abstract

We give function space realizations of all representations of the conformal superalgebra su(2,2/N) and of the supergroup SU(2, 2 /N) induced from irreducible finite-dimensional Lorentz and SU(N) representations realized without spin and isospin indices. We use the lowest weight module structure of our su(2,2/N) representations to present a general procedure (adapted from the semisimple Lie algebra case) for the canonical construction of invariant differential operators closely related to the reducible (indecomposable) representations. All conformal supercovariant derivatives are obtained in this way. Examples of higher order invariant differential operators are given.