Reflection group diagrams for a sequence of Gaussian Lorentzian lattices

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2017-01-01
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Goertz, Jeremiah
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Tathagata Basak
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Altmetrics
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Mathematics
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We exhibit a set of three related Gaussian Lorentzian lattices with ``Coxeter-like'' root diagrams. These root diagrams possess a point of symmetry in complex hyperbolic space, similar to the Weyl vector for positive-definite $\Z$-lattices. For two of the three lattices, this point of symmetry is used to show that the reflections in the diagram roots generate the lattice's reflection group. It is shown for all three lattices that the lattice's reflection group has finite index in its automorphism group.

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Sun Jan 01 00:00:00 UTC 2017