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

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

2009-01-15

arxiv.org/abs/0901.2280v1

Mathematics

Representation Theory

13 pages, 1 figure

Scientific paper

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^+.

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