A classification of subsystems of a root system

Details A classification of subsystems of a root system A classification of subsystems of a root system

2006-11-29

arxiv.org/abs/math/0611904v4

Mathematics

Representation Theory

47 pages, corrected an error in the Table

Scientific paper

We classify isomorphic classes of the homomorphisms of a root system $\Xi$ to a root system $\Sigma$ which do not change Cartan integers. We examine several types of isomorphic classes defined by the Weyl group of $\Sigma$, that of $\Xi$ and the automorphisms of $\Sigma$ or $\Xi$ etc. We also distinguish the subsystem generated by a subset of a fundamental system. We introduce the concept of the dual pair for root systems which helps to study the action of the outer automorphism of $\Xi$ on the homomorphisms.

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