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

Article

Journal

Archiv der Mathematik

Volume

123

Pages

567–583

No. of pages

17

ISSN

0003-889X

Publication date

12.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.1007/s00013-024-02046-1 (Access: Open)
https://doi.org/10.48550/arXiv.2404.00278 (Access: Open)