An easy proof of the Stone–von Neumann–Mackey Theorem

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 Rn. A theorem of Pontryagin and van Kampen on the structure of locally compact abelian groups (which is evident in any particular case) is assumed.