An easy proof of the Stone-von Neumann-Mackey theorem
arXiv:0912.0574 · doi:10.1016/j.exmath.2010.06.001
Abstract
The Stone-von Neumann-Mackey Theorem for Heisenberg groups associated to locally compact abelian groups is proved using the Peter-Weyl theorem and the theory of Fourier transforms for finite dimensional real vector spaces. A theorem of Pontryagin and van Kampen on the structure of locally compact abelian groups (which is evident in any particular case) is assumed.
10 pages