2024/03/30 by Cuntz, Michael, Mühlherr, Bernhard
#16T30 #17B22 #52C35 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2404.00278
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.