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arXiv · 2104.14890

Towards canonical representations of finite Heisenberg groups

Sergey Lysenko
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Abstract

We consider a finite abelian group $M$ of odd exponent $n$ with a symplectic form $\omega: M\times M\to \mu_n$ and the Heisenberg extension $1\to \mu_n\to H\to M\to 1$ with the commutator $\omega$. According to the Stone - von Neumann theorem, $H$ admits an irreducible representation with the tautological central character (defined up to a non-unique isomorphism). We construct such irreducible representation of $H$ defined up to a unique isomorphism, so canonical in this sense.

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BibTeXRIS

Sergey Lysenko. 2021-04-30. Towards canonical representations of finite Heisenberg groups. https://doi.org/10.24033/bsmf.2855

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