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.
Domains
Representation Theory [math.RT]
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