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arXiv · 2206.03779

A colourful classification of (quasi) root systems and hyperplane arrangements

Gabriele Rembado
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Abstract

We introduce a class of graphs with coloured edges to encode subsystems of the classical root systems, which in particular classify them up to equivalence. We further use the graphs to describe root-kernel intersections, as well as restrictions of root (sub)systems on such intersections, generalising the regular part of a Cartan subalgebra. We also consider a slight variation to encode the hyperplane arrangements only, showing there is a unique noncrystallographic arrangement that arises. Finally, a variation of the main definition leads to elementary classifications of closed and Levi root subsystems.

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Gabriele Rembado. 2022-06-08. A colourful classification of (quasi) root systems and hyperplane arrangements. https://arxiv.org/abs/2206.03779

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