Journal of Lie Theory 34 (2024), No. 2, 385--422
Copyright Heldermann Verlag 2024
A Colourful Classification of (Quasi) Root Systems and Hyperplane Arrangements
Gabriele Rembado
Institut Montpelliérain A. Grothendieck, University of Montpellier, Montpellier, France
gabriele.rembado@umontpellier.fr
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.
Keywords: Root subsystems, Levi subsystems, graphs, hyperplane arrangements.
MSC: 17B22, 52C35.
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