Generalized root systems

by Philipp Peter Lehnhardt (Justus-Liebig-Universität Giessen)

Monday 9 Feb 2026, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

Generalized root systems (GRS) unite different generalizations of root systems in one concept. We call a finite, non-empty subset Φ of a Euclidean vector space E a GRS if for every α,β∈Φ:

1. α⋅β>0⇒α−β∈Φ
2. α⋅β=0⇒[α−β∈Φ⇔α+β∈Φ]

These properties are preserved under factoring roots out of a GRS (which we call quotient taking). M. Cuntz and B. Mühlherr used the classification of crystallographic arrangements to prove that every GRS of rank ≥2 is equivalent to a quotient of a classical root system.
My talk will concern my current work on proving this same result in an elementary fashion without relying on advanced results.