A classification of generalized root systems

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.