The minimal representation of the conformal group and classic solutions to the wave equation

Hunziker, Markus; Sepanski, Mark R.; Stanke, Ronald J.

The minimal representation of the conformal group and classic solutions to the wave equation

Authors

Hunziker, Markus

Sepanski, Mark R.

Stanke, Ronald J.

Description

We give a uniform realization of the minimal representation of a double cover of the conformal group SO(2,n+1)_0 in the kernel of the wave operator on flat Minkowski space as a positive energy representation H^+ for n even and odd. Using this realization, we obtain an explicit orthonormal basis for H^+ that is well behaved with respect to energy and angular momentum. Of special note, for n odd, all functions in our basis are rational functions. Finally, using Fourier analysis with respect to this basis, we prove that every classical real-valued solution to the wave equation is the real part of a unique continuous element in the representation H^+.
13 pages, 1 figure