Geodesic
A Colourful Classification of (Quasi) Root Systems and Hyperplane Arrangements
Journal of Lie theory, Tome 34 (2024) no. 2, pp. 385-422
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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.
Classification : 17B22, 52C35
Mots-clés : Root subsystems, Levi subsystems, graphs, hyperplane arrangements 
@article{JLT_2024_34_2_JLT_2024_34_2_a5,
     author = {G. Rembado},
     title = {A {Colourful} {Classification} of {(Quasi)} {Root} {Systems} and {Hyperplane} {Arrangements}},
     journal = {Journal of Lie theory},
     pages = {385--422},
     year = {2024},
     volume = {34},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2024_34_2_JLT_2024_34_2_a5/}
}
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G. Rembado. A Colourful Classification of (Quasi) Root Systems and Hyperplane Arrangements. Journal of Lie theory, Tome 34 (2024) no. 2, pp. 385-422. http://geodesic.mathdoc.fr/item/JLT_2024_34_2_JLT_2024_34_2_a5/