LieTypes : Table of Contents

• LieTypes -- Common types for Lie groups and Lie algebras
• 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
• cartanMatrix -- Provide the Cartan matrix of a simple Lie algebra
• casimirScalar -- computes the scalar by which the Casimir operator acts on an irreducible Lie algebra module
• 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
• dualCoxeterNumber -- returns the dual Coxeter number of a simple Lie algebra
• dynkinDiagram -- Provide the Dynkin diagram of a simple Lie algebra
• fusionCoefficient -- 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
• highestRoot -- returns the highest root of a simple Lie algebra
• irreducibleLieAlgebraModule -- construct the irreducible Lie algebra module with given highest weight
• isIrreducible -- Whether a Lie algebra module is irreducible or not
• killingForm -- computes the scaled Killing form applied to two weights
• LieAlgebra -- class for Lie algebras
• LieAlgebra ++ LieAlgebra -- Take the direct sum of 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
• LieAlgebraModule @ LieAlgebraModule -- Take the tensor product of modules over different Lie algebras
• LieAlgebraModule ^** ZZ -- Computes the nth tensor power of a Lie algebra module
• LieAlgebraModuleFromWeights -- finds a Lie algebra module based on its weights
• multiplicity(List,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module
• new LieAlgebra from Matrix -- Define a Lie algebra from its Cartan matrix
• positiveRoots -- returns the positive (co)roots of a simple Lie algebra
• qdim -- Compute principal specialization of character or quantum dimension
• simpleLieAlgebra -- construct a simple Lie algebra
• simpleRoots -- returns the simple roots of a simple Lie algebra
• starInvolution -- computes w* for a weight w
• subLieAlgebra -- Define a sub-Lie algebra of an existing one
• symmetricPower(ZZ,LieAlgebraModule) -- Computes the nth symmetric / exterior tensor power of a Lie algebra module
• tensorCoefficient -- computes the multiplicity of W in U tensor V
• trivialModule -- The trivial module of a Lie algebra
• 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