LieAlgebraModule -- class for Lie algebra modules

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

o1 = g

o1 : simple LieAlgebra

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

o2 = M

o2 : irreducible LieAlgebraModule over g

Functions and methods returning an object of class LieAlgebraModule :

• adams -- Computes the action of the nth Adams operator on a Lie algebra module
• adjointModule -- The adjoint module of a Lie algebra
• branchingRule -- A Lie algebra module viewed as a module over a Lie subalgebra
• fusionProduct -- computes the multiplicities of irreducibles in the decomposition of the fusion product of U and V
• irreducibleLieAlgebraModule -- construct the irreducible Lie algebra module with given highest weight
• LieAlgebraModuleFromWeights -- finds a Lie algebra module based on its weights
• trivialModule -- The trivial module of a Lie algebra

Methods that use an object of class LieAlgebraModule :

• adams(ZZ,LieAlgebraModule) -- see adams -- Computes the action of the nth Adams operator on a Lie algebra module
• branchingRule(LieAlgebraModule,LieAlgebra) -- see branchingRule -- A Lie algebra module viewed as a module over a Lie subalgebra
• branchingRule(LieAlgebraModule,List) -- see branchingRule -- A Lie algebra module viewed as a module over a Lie subalgebra
• branchingRule(LieAlgebraModule,Matrix) -- see branchingRule -- A Lie algebra module viewed as a module over a Lie subalgebra
• casimirScalar(LieAlgebraModule) -- see casimirScalar -- computes the scalar by which the Casimir operator acts on an irreducible Lie algebra module
• character(LieAlgebraModule) -- see character -- Computes the character of a Lie algebra module
• dim(LieAlgebraModule) -- computes the dimension of a Lie algebra module as a vector space over the ground field
• 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
• isIrreducible(LieAlgebraModule) -- see isIrreducible -- Whether a Lie algebra module is irreducible or not
• LieAlgebraModule ** LieAlgebraModule -- tensor product of LieAlgebraModules
• directSum(LieAlgebraModule) -- see LieAlgebraModule ++ LieAlgebraModule -- direct sum of LieAlgebraModules
• LieAlgebraModule ++ LieAlgebraModule -- direct sum of LieAlgebraModules
• LieAlgebraModule @ LieAlgebraModule -- Take the tensor product of modules over different Lie algebras
• LieAlgebraModule ^ ZZ (missing documentation)
• LieAlgebraModule ^** ZZ -- Computes the nth tensor power of a Lie algebra module
• LieAlgebraModule _ ZZ (missing documentation)
• LieAlgebraModule _* (missing documentation)
• qdim(LieAlgebraModule) -- see qdim -- Compute principal specialization of character or quantum dimension
• qdim(LieAlgebraModule,ZZ) -- see qdim -- Compute principal specialization of character or quantum dimension
• dual(LieAlgebraModule) -- see starInvolution -- computes w* for a weight w
• starInvolution(LieAlgebraModule) -- see starInvolution -- computes w* for a weight w
• exteriorPower(ZZ,LieAlgebraModule) -- see symmetricPower(ZZ,LieAlgebraModule) -- Computes the nth symmetric / exterior tensor power of a Lie algebra module
• symmetricPower(ZZ,LieAlgebraModule) -- Computes the nth symmetric / exterior tensor power of a Lie algebra module
• 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.