XXXVII Workshop on Geometric Methods in Physics | 1-7.07.2018 |

VII School on Geometry and Physics | 25-29.06.2018 |

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## Patrick Moylan## Heisenberg-Weyl Algebras and Representations of Poincar\'e GroupsWe give a novel description of unitary irreducible representations of the Poincar\'e groups in 2, 3 and 4 space-time dimensions as unitary operators on the representation spaces of the Schr\"odinger representation of the Heisenberg-Weyl algebra ${\bf W}_n(\mathbb{R})$ of index $n$ = 1, 2, and 3, respectively. We relate this approach to the usual method of describing the representations of Poincar\'e groups, i.e. the Wigner-Mackey construction. |

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