A classification of generalized root systems

authored by

Michael Cuntz, B. Mühlherr

Abstract

Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture that every generalized root system is equivalent to one associated to a restriction of a Weyl arrangement. In this note we prove the conjecture and provide a complete classification of generalized root systems up to equivalence.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Justus Liebig University Giessen

Type

Preprint

No. of pages

11

Publication date

25.07.2024

Publication status

Accepted/In press

Electronic version(s)

https://arxiv.org/abs/2404.00278 (Access: Open)