multiplicity(List,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module

Synopsis

• Function: multiplicity

• Usage:

  multiplicity(v,M)

• Inputs:
  • v, a list,
  • M, an instance of the type LieAlgebraModule,
• Optional inputs:
  • BasisElementLimit => ..., default value infinity,
  • DegreeLimit => ..., default value {},
  • MinimalGenerators => ..., default value true,
  • PairLimit => ..., default value infinity,
  • Strategy => ..., default value null,
  • Variable => ..., default value "w",
• Outputs:
  • k, an integer,

Description

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

o1 = g

o1 : simple LieAlgebra

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

o2 = V

o2 : irreducible LieAlgebraModule over g

i3 : multiplicity({-1,1},V)

o3 = 2

See also

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