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

Gabriele Rembado
2022 arXiv   pre-print
We will introduce a class of graphs with coloured edges to encode root subsystems of the classical root systems, which in particular classify them up to the Weyl-group action, extending a previous construction for subsystems obtained from fission (which in turn are related to deformations of moduli spaces of meromorphic connections). We will further use these graphs to describe root-kernel intersections, as well as a natural quotient operation that corresponds to taking restrictions of root
more » ... )systems on such intersections, so that the complement of the resulting hyperplanes generalises the regular part of a Cartan subalgebra. Finally we will consider a slight variation of the above to encode the hyperplane arrangements only, showing there is a unique noncrystallographic such arrangement that arises.
arXiv:2206.03779v1 fatcat:2alld25rprh6jfzxu6fpddbc4q