plot the Dynkin diagram for a given root type - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : DifferentialGeometry : LieAlgebras : DifferentialGeometry/LieAlgebras/DynkinDiagram

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"

       m         - a positive integer

       version   - 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  Am , Bm ,  Cm ,  Dm , E6 , E7 , E8 , F4 , G2 .

• 

 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

withDifferentialGeometry:withLieAlgebras:

 

Example 1.

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

DynkinDiagramA,6

DynkinDiagramB,6

DynkinDiagramC,6

DynkinDiagramD,6

 

Example 2.

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

DynkinDiagramF,4

DynkinDiagramG,2

 

Example 3. For the exceptional roots systems E6, E7, E8  there are two different conventions for the labelling of the roots. Either one can be plotted using the keyword argument version. The default is version = 1.

DynkinDiagramE,8

DynkinDiagramE,8,version=2

 

 

 

See Also

DifferentialGeometry, CartanMatrix, Cartan Matrix Details, RootSpaceDecomposition, SimpleRoots, SatakeDiagram


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam