 DynkinDiagram - Maple Help

LieAlgebras[DynkinDiagram] - plot the Dynkin diagram for a given root type

Calling Sequences

DynkinDiagram( RT, m, option)

Parameters

RT                   - a string, denoting a root type "A", "B', "C", "D", "E", "F", "G"

- a positive integer

- optional, the integer 1 or 2 Description

 • The Dynkin diagram is a graphic means of describing abstract root systems or, equivalently, of characterizing Cartan matrices. The command DynkinDiagram plots the Dynkin diagram for each root type , , , , , , , , .
 • See Details of Cartan Matrices and Dynkin Diagrams for more information on the relationship between these two ways of characterizing complex simple Lie algebras.
 • For real Lie algebras, the Satake diagrams provide the counterpart to the Dynkin diagrams. Examples

 > $\mathrm{with}\left(\mathrm{DifferentialGeometry}\right):$$\mathrm{with}\left(\mathrm{LieAlgebras}\right):$

Example 1.

Here are the Dynkin diagrams for each classical root type of rank 6.

 > $\mathrm{DynkinDiagram}\left("A",6\right)$ > $\mathrm{DynkinDiagram}\left("B",6\right)$ > $\mathrm{DynkinDiagram}\left("C",6\right)$ > $\mathrm{DynkinDiagram}\left("D",6\right)$ Example 2.

Here are the Dynkin diagrams for two of the exceptional root systems.

 > $\mathrm{DynkinDiagram}\left("F",4\right)$ > $\mathrm{DynkinDiagram}\left("G",2\right)$ Example 3. For the exceptional roots systems there are two different conventions for the labelling of the roots. Either one can be plotted using the keyword argument $\mathrm{version}$. The default is

 > $\mathrm{DynkinDiagram}\left("E",8\right)$ > $\mathrm{DynkinDiagram}\left("E",8,\mathrm{version}=2\right)$ 