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weightDiagram -- computes the weights in a Lie algebra module and their multiplicities

Description

Let $V$ be the irreducible $\mathbf{g}$-module with highest weight $v$. This function returns a tally whose keys are the weights appearing in $V$ and whose values are the multiplicities of these weights. An optional argument "Strategy" allows to specify which algorithm to use, see character.

i1 : g=simpleLieAlgebra("A",2)

o1 = g

o1 : simple LieAlgebra
 
i2 : V=irreducibleLieAlgebraModule({2,1},g)

o2 = V

o2 : irreducible LieAlgebraModule over g
 
i3 : weightDiagram(V)

o3 = VirtualTally{{-1, -2} => 1}
                  {-1, 1} => 2
                  {-2, 0} => 1
                  {-2, 3} => 1
                  {-3, 2} => 1
                  {0, -1} => 2
                  {0, 2} => 1
                  {1, -3} => 1
                  {1, 0} => 2
                  {2, -2} => 1
                  {2, 1} => 1
                  {3, -1} => 1

o3 : VirtualTally

See also

Ways to use weightDiagram:

  • weightDiagram(LieAlgebra,List)
  • weightDiagram(LieAlgebra,Vector)
  • weightDiagram(LieAlgebraModule)

For the programmer

The object weightDiagram is a method function with options.

The source of this document is in LieAlgebraRepresentations/documentation.m2:791:0.