关于根系的基

ON THE BASE OF A ROOT SYSTEM

设φ是不可约根系,△是φ的基,G(△)是φ的Dynkin图,我们先给出φ的特殊子集X的定义,对这样的X再定义一个图G(X),得到定理 X(?)φ,则X是φ的基的充要条件是X是特殊的,且图G(X)与G(△)同构.

Let Φ be an irreducible root system, Δ be a base of Φ, and C(Δ) be the Dynkin graph of Φ. This paper gives the definition of special subsets of Φ. and for a special subset X of Φ, and gives a graph G(X) relative to X. Then the following result is obtained:Theorem Let X be a subset of Φ, then X is a base of Φ if and only if X is special and G(X) is isomorphic to G(Δ).