LieAlgebraModule -- class for Lie algebra modules

Description

This class represents Lie algebra modules. Currently only modules over simple Lie algebras over the complex numbers are supported. An object of type LieAlgebraModule is a hash table recording the Lie algebra and the decomposition of the module into irreducible Lie algebra modules, which are indexed by their highest weights.

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

o1 = g

o1 : LieAlgebra

i2 : M=irreducibleLieAlgebraModule({1,1},g)

o2 = M

o2 : g module

Functions and methods returning an object of class LieAlgebraModule :

irreducibleLieAlgebraModule -- construct the irreducible Lie algebra module with given highest weight

Methods that use an object of class LieAlgebraModule :

"casimirScalar(LieAlgebraModule)" -- see casimirScalar -- computes the scalar by which the Casimir operator acts on an irreducible Lie algebra module
dim(LieAlgebraModule) -- computes the dimension of a Lie algebra module as a vector space over the ground field
expression(LieAlgebraModule) (missing documentation)
"fusionCoefficient(LieAlgebraModule,LieAlgebraModule,LieAlgebraModule,ZZ)" -- see fusionCoefficient -- computes the multiplicity of W in the fusion product of U and V
"fusionProduct(LieAlgebraModule,LieAlgebraModule,ZZ)" -- see fusionProduct -- computes the multiplicities of irreducibles in the decomposition of the fusion product of U and V
"isIsomorphic(LieAlgebraModule,LieAlgebraModule)" -- see isIsomorphic -- tests whether two Lie algebra modules are isomorphic
LieAlgebraModule ** LieAlgebraModule -- tensor product of LieAlgebraModules
LieAlgebraModule ++ LieAlgebraModule -- direct sum of LieAlgebraModules
multiplicity(List,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module
net(LieAlgebraModule) (missing documentation)
"tensorCoefficient(LieAlgebraModule,LieAlgebraModule,LieAlgebraModule)" -- see tensorCoefficient -- computes the multiplicity of W in U tensor V
"weightDiagram(LieAlgebraModule)" -- see weightDiagram -- computes the weights in a Lie algebra module and their multiplicities

For the programmer

The object LieAlgebraModule is a type, with ancestor classes HashTable < Thing.