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A Euclidean interpretation of Dynkin diagrams and its relation to root systems

✍ Scribed by Daniel Drucker; Daniel Frohardt

Publisher
Springer
Year
1987
Tongue
English
Weight
448 KB
Volume
22
Category
Article
ISSN
0046-5755

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✦ Synopsis

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 semideflnite 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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