Characters of the Poincaré Group

Abstract

We calculate the characters of the Poincaré group P̄ as solutions of differential equations in a way which is valid for a large class of Lie groups. We discuss the solutions of linear differential equations on an analytic manifold in a space of distributions. Then, we calculate the characters of SL(2, R) and the central distributions on P̄. Finally, we give the characters of all unitary irreducible representations of P̄, including mass 0, and some expressions which may be ``characters'' of nonunitary representations.