root system

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  • noun

Synonyms for root system

a developed system of roots

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Let g be a simple Lie algebra over C with Dynkin diagram [delta].
We number the nodes of its Dynkin diagram as in Figure 2.
What makes type E more difficult than type D is that there are many nodes of the Dynkin diagram with labels [a.
6] However log-concavity is no longer sufficient to establish positivity at some inner nodes of the Dynkin diagram, and some stronger form of log-concavity would be necessary.
In the previous section, only the Dynkin diagram A2n is considered.
The subset K [subset or equal to] [DELTA] is drawn as a marked set of vertices in the Dynkin diagram which is compared to the Dynkin diagram for [D.
This ordering is expressed in the Dynkin diagrams in Figure 2.
infinity]] denote the Dynkin diagram depicted below:
1 We get similar results for infinite Dynkin diagrams [Dsub.
Any automorphism [tau] of the affine Dynkin diagram [GAMMA] induces a symmetry of [bar.
r]) in that paper), where r is a node in the classical Dynkin diagram and s is a positive integer.
Let [GAMMA] = (I, E) be its Dynkin diagram, where I is the set of vertices and E the set of edges.
union] {[infinity]} and we consider the Coxeter system (W, S) corresponding to the linear Dynkin diagram [[GAMMA].
The Dynkin diagram r associated to (W, S) is the graph with vertex set S and, for each pair s, t with [m.
In Figure 1, we fix a Dynkin diagram on the left, and we give two examples of words with the corresponding heaps.