= Stone-von Neumann theorem
{c}
Every irreducible strongly continuous representation of the <Weyl relations> with fixed nonzero central character is unitarily equivalent to the translation-modulation representation on $L^2(\mathbb R)$. The <Gaussian projection in a Weyl representation> supplies a cyclic vector whose Weyl-orbit inner products agree with those of a Gaussian in the standard representation. Matching those orbit vectors gives the unitary intertwiner, with no appeal to a classification assertion in place of the proof.
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