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Preprints, Working Papers, ... Year : 2021

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 ω : M × M → µn and the Heisenberg extension 1 → µn → H → M → 1 with the commutator ω. 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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Dates and versions

hal-03281569 , version 1 (08-07-2021)

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Sergey Lysenko. Towards canonical representations of finite Heisenberg groups. 2021. ⟨hal-03281569⟩
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