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arXiv · 1311.0341

A Symplectic Representation of $\mathrm{E}_7$

Tevian Dray·Corinne A. Manogue·Robert A. Wilson
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Abstract

We explicitly construct a particular real form of the Lie algebra $\mathfrak{e}_7$ in terms of symplectic matrices over the octonions, thus justifying the identifications $\mathfrak{e}_7\cong\mathfrak{sp}(6,\mathbb{O})$ and, at the group level, $\mathrm{E}_7\cong\mathrm{Sp}(6,\mathbb{O})$. Along the way, we provide a geometric description of the minimal representation of $\mathfrak{e}_7$ in terms of rank 3 objects called cubies.

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Tevian Dray, Corinne A. Manogue, Robert A. Wilson. 2013-11-02. A Symplectic Representation of $\mathrm{E}_7$. https://arxiv.org/abs/1311.0341

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