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LieAlgebras[DynkinDiagram] - plot the Dynkin diagram for a given root type
Calling Sequences
DynkinDiagram(, )
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 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
Example 1.
Here are the Dynkin diagrams for each classical root type of rank 6.
Example 2.
Here are the Dynkin diagrams for two of the exceptional root systems.
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 . The default is
See Also
DifferentialGeometry, CartanMatrix, Cartan matricesDetails, RootSpaceDecomposition, SimpleRoots, SatakeDiagram
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