Abstract
A simple metric property satisfied by bases of (finite, not necessarily reduced) root systems is used to define sets in Euclidean space that provide models for Dynkin diagrams and their positive semidefinite one-vertex extensions. The theory of root systems can be founded on the study of these ‘Dynkin sets’, and conversely the Dynkin sets representing connected diagrams can be characterized as the bases and extended bases of root systems. (By an ‘extended base’, we mean a base together with the lowest root of a given length.) In this correspondence the role of nonreduced root systems is natural and important.
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Drucker, D., Frohardt, D. A Euclidean interpretation of Dynkin diagrams and its relation to root systems. Geom Dedicata 22, 77–85 (1987). https://doi.org/10.1007/BF00183054
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DOI: https://doi.org/10.1007/BF00183054