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
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Description
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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 , , , , , , , , .
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For real Lie algebras, the Satake diagrams provide the counterpart to the Dynkin diagrams.
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Examples
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Example 1.
Here are the Dynkin diagrams for each classical root type of rank 6.
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Example 2.
Here are the Dynkin diagrams for two of the exceptional root systems.
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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
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