LieTypes : Table of Contents

• LieTypes -- Common types for Lie groups and Lie algebras
• 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
• dualCoxeterNumber -- 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.
• 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.
• highestRoot -- returns the highest root of a simple Lie algebra
• irreducibleLieAlgebraModule -- construct the irreducible Lie algebra module with given highest weight
• isIsomorphic -- tests whether two Lie algebra modules are isomorphic
• KillingForm -- 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
• 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
• positiveRoots -- returns the positive roots of a simple Lie algebra
• simpleLieAlgebra -- construct a simple Lie algebra
• starInvolution -- computes w* for a weight w
• tensorCoefficient -- computes the multiplicity of W in U tensor V
• weightDiagram -- computes the weights in a Lie algebra module and their multiplicities
• weylAlcove -- the dominant integral weights of level less than or equal to l