LieTypes : Index
- casimirScalar -- computes the scalar by which the Casimir operator acts on an irreducible Lie algebra module
- casimirScalar(LieAlgebraModule) -- computes the scalar by which the Casimir operator acts on an irreducible Lie algebra module
- casimirScalar(String,ZZ,List) -- 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
- dualCoxeterNumber -- returns the dual Coxeter number of a simple Lie algebra
- dualCoxeterNumber(LieAlgebra) -- returns the dual Coxeter number of a simple Lie algebra
- dualCoxeterNumber(String,ZZ) -- returns the dual Coxeter number of a simple Lie algebra
- fusionCoefficient -- computes the multiplicity of W in the fusion product of U and V
- fusionCoefficient(..., MaxWordLength => ...) -- Optional argument to specify the allowable length of words in the affine Weyl group when computing fusion products.
- fusionCoefficient(LieAlgebraModule,LieAlgebraModule,LieAlgebraModule,ZZ) -- computes the multiplicity of W in the fusion product of U and V
- fusionProduct -- computes the multiplicities of irreducibles in the decomposition of the fusion product of U and V
- fusionProduct(..., MaxWordLength => ...) -- Optional argument to specify the allowable length of words in the affine Weyl group when computing fusion products.
- fusionProduct(LieAlgebraModule,LieAlgebraModule,ZZ) -- computes the multiplicities of irreducibles in the decomposition of the fusion product of U and V
- highestRoot -- returns the highest root of a simple Lie algebra
- highestRoot(LieAlgebra) -- returns the highest root of a simple Lie algebra
- highestRoot(String,ZZ) -- returns the highest root of a simple Lie algebra
- irreducibleLieAlgebraModule -- construct the irreducible Lie algebra module with given highest weight
- irreducibleLieAlgebraModule(List,LieAlgebra) -- construct the irreducible Lie algebra module with given highest weight
- isIsomorphic -- tests whether two Lie algebra modules are isomorphic
- isIsomorphic(LieAlgebraModule,LieAlgebraModule) -- tests whether two Lie algebra modules are isomorphic
- KillingForm -- computes the scaled Killing form applied to two weights
- KillingForm(LieAlgebra,List,List) -- computes the scaled Killing form applied to two weights
- KillingForm(String,ZZ,List,List) -- computes the scaled Killing form applied to two weights
- LieAlgebra -- class for Lie algebras
- LieAlgebra == LieAlgebra -- tests equality of LieAlgebra
- LieAlgebraModule -- class for Lie algebra modules
- LieAlgebraModule ** LieAlgebraModule -- tensor product of LieAlgebraModules
- LieAlgebraModule ++ LieAlgebraModule -- direct sum of LieAlgebraModules
- LieTypes -- Common types for Lie groups and Lie algebras
- MaxWordLength -- Optional argument to specify the allowable length of words in the affine Weyl group when computing fusion products.
- multiplicity(List,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module
- simpleLieAlgebra -- construct a simple Lie algebra
- simpleLieAlgebra(String,ZZ) -- construct a simple Lie algebra
- starInvolution -- computes w* for a weight w
- starInvolution(List,LieAlgebra) -- computes w* for a weight w
- starInvolution(String,ZZ,List) -- computes w* for a weight w
- tensorCoefficient -- computes the multiplicity of W in U tensor V
- tensorCoefficient(LieAlgebraModule,LieAlgebraModule,LieAlgebraModule) -- computes the multiplicity of W in U tensor V
- weightDiagram -- computes the weights in a Lie algebra module and their multiplicities
- weightDiagram(LieAlgebraModule) -- computes the weights in a Lie algebra module and their multiplicities
- weightDiagram(String,ZZ,List) -- computes the weights in a Lie algebra module and their multiplicities
- weylAlcove -- the dominant integral weights of level less than or equal to l
- weylAlcove(String,ZZ,ZZ) -- the dominant integral weights of level less than or equal to l
- weylAlcove(ZZ,LieAlgebra) -- the dominant integral weights of level less than or equal to l