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Towards canonical representations of finite Heisenberg groups

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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Preprints, Working Papers, ...
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https://hal.univ-lorraine.fr/hal-03281569
Contributor : Sergey Lysenko <>
Submitted on : Thursday, July 8, 2021 - 12:37:05 PM
Last modification on : Friday, July 9, 2021 - 4:30:23 AM

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  • HAL Id : hal-03281569, version 1
  • ARXIV : 2104.14890

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

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