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

Autor:	Rembado, Gabriele
Rok vydání:	2022
Předmět:	Mathematics - Rings and Algebras Mathematics - Combinatorics Mathematics - Representation Theory 17B22 52C35
Zdroj:	Journal of Lie Theory 34 (2024), No. 2, 385--422
Druh dokumentu:	Working Paper
Popis:	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. Comment: v2: added two sections about closed and Levi root subsystems. 46 pages, 64 figures; comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.03779 Zobrazit plný text záznamu View this record from Arxiv