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arXiv · 2211.03707

A causal characterisation of $\mathrm{Sp}_{\mathrm{ell}}^{+}(2n)$

Jakob Hedicke
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Abstract

We show that the natural conjugation invariant cone structure on the linear symplectic group $\mathrm{Sp}(2n)$ is globally hyperbolic in the positively elliptic region $\mathrm{Sp}_{\mathrm{ell}}^{+}(2n)$. This answers a question by Abbondandolo, Benedetti and Polterovich and shows a formula for a bi-invariant Lorentzian distance function dened by these authors for elements in this region. Moreover we give a characterisation of the positively elliptic region and of $-id \in\mathrm{Sp}(2n)$ in terms of the causality of this cone structure.

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Jakob Hedicke. 2022-11-07. A causal characterisation of $\mathrm{Sp}_{\mathrm{ell}}^{+}(2n)$. https://arxiv.org/abs/2211.03707

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