LieTypes : Index
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adams -- Computes the action of the nth Adams operator on a Lie algebra module
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adams(ZZ,LieAlgebraModule) -- Computes the action of the nth Adams operator on a Lie algebra module
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adjointModule -- The adjoint module of a Lie algebra
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adjointModule(LieAlgebra) -- The adjoint module of a Lie algebra
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branchingRule -- A Lie algebra module viewed as a module over a Lie subalgebra
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branchingRule(LieAlgebraModule,LieAlgebra) -- A Lie algebra module viewed as a module over a Lie subalgebra
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branchingRule(LieAlgebraModule,List) -- A Lie algebra module viewed as a module over a Lie subalgebra
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branchingRule(LieAlgebraModule,Matrix) -- A Lie algebra module viewed as a module over a Lie subalgebra
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cartanMatrix -- Provide the Cartan matrix of a simple Lie algebra
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cartanMatrix(LieAlgebra) -- Provide the Cartan matrix of a simple Lie algebra
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casimirScalar -- computes the scalar by which the Casimir operator acts on an irreducible Lie algebra module
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casimirScalar(LieAlgebraModule) -- computes the scalar by which the Casimir operator acts on an irreducible Lie algebra module
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character -- Computes the character of a Lie algebra module
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character(...,Strategy=>...) -- Computes the character of a Lie algebra module
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character(LieAlgebra,List) -- Computes the character of a Lie algebra module
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character(LieAlgebra,Vector) -- Computes the character of a Lie algebra module
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character(LieAlgebraModule) -- Computes the character of a Lie algebra module
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dim(LieAlgebraModule) -- computes the dimension of a Lie algebra module as a vector space over the ground field
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directSum(LieAlgebra) -- Take the direct sum of Lie algebras
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directSum(LieAlgebraModule) -- direct sum of LieAlgebraModules
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dual(LieAlgebraModule) -- computes w* for a weight w
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dualCoxeterNumber -- returns the dual Coxeter number of a simple Lie algebra
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dualCoxeterNumber(LieAlgebra) -- returns the dual Coxeter number of a simple Lie algebra
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dualCoxeterNumber(String,ZZ) -- returns the dual Coxeter number of a simple Lie algebra
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dynkinDiagram -- Provide the Dynkin diagram of a simple Lie algebra
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dynkinDiagram(LieAlgebra) -- Provide the Dynkin diagram of a simple Lie algebra
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exteriorPower(ZZ,LieAlgebraModule) -- Computes the nth symmetric / exterior tensor power of a Lie algebra module
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fusionCoefficient -- computes the multiplicity of W in the fusion product of U and V
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fusionCoefficient(LieAlgebraModule,LieAlgebraModule,LieAlgebraModule,ZZ) -- computes the multiplicity of W in the fusion product of U and V
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fusionProduct -- computes the multiplicities of irreducibles in the decomposition of the fusion product of U and V
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fusionProduct(LieAlgebraModule,LieAlgebraModule,ZZ) -- computes the multiplicities of irreducibles in the decomposition of the fusion product of U and V
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highestRoot -- returns the highest root of a simple Lie algebra
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highestRoot(LieAlgebra) -- returns the highest root of a simple Lie algebra
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irreducibleLieAlgebraModule -- construct the irreducible Lie algebra module with given highest weight
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irreducibleLieAlgebraModule(List,LieAlgebra) -- construct the irreducible Lie algebra module with given highest weight
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irreducibleLieAlgebraModule(Vector,LieAlgebra) -- construct the irreducible Lie algebra module with given highest weight
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isIrreducible -- Whether a Lie algebra module is irreducible or not
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isIrreducible(LieAlgebraModule) -- Whether a Lie algebra module is irreducible or not
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killingForm -- computes the scaled Killing form applied to two weights
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killingForm(LieAlgebra,List,List) -- computes the scaled Killing form applied to two weights
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killingForm(LieAlgebra,Vector,Vector) -- computes the scaled Killing form applied to two weights
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LieAlgebra -- class for Lie algebras
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LieAlgebra ++ LieAlgebra -- Take the direct sum of Lie algebras
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LieAlgebra == LieAlgebra -- tests equality of LieAlgebra
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LieAlgebraModule -- class for Lie algebra modules
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LieAlgebraModule ** LieAlgebraModule -- tensor product of LieAlgebraModules
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LieAlgebraModule ++ LieAlgebraModule -- direct sum of LieAlgebraModules
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LieAlgebraModule @ LieAlgebraModule -- Take the tensor product of modules over different Lie algebras
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LieAlgebraModule ^** ZZ -- Computes the nth tensor power of a Lie algebra module
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LieAlgebraModuleFromWeights -- finds a Lie algebra module based on its weights
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LieAlgebraModuleFromWeights(RingElement,LieAlgebra) -- finds a Lie algebra module based on its weights
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LieAlgebraModuleFromWeights(VirtualTally,LieAlgebra) -- finds a Lie algebra module based on its weights
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LieTypes -- Common types for Lie groups and Lie algebras
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LL -- construct the irreducible Lie algebra module with given highest weight
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multiplicity(List,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module
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multiplicity(Vector,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module
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new LieAlgebra from Matrix -- Define a Lie algebra from its Cartan matrix
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positiveCoroots -- returns the positive (co)roots of a simple Lie algebra
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positiveCoroots(LieAlgebra) -- returns the positive (co)roots of a simple Lie algebra
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positiveRoots -- returns the positive (co)roots of a simple Lie algebra
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positiveRoots(LieAlgebra) -- returns the positive (co)roots of a simple Lie algebra
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qdim -- Compute principal specialization of character or quantum dimension
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qdim(LieAlgebraModule) -- Compute principal specialization of character or quantum dimension
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qdim(LieAlgebraModule,ZZ) -- Compute principal specialization of character or quantum dimension
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simpleLieAlgebra -- construct a simple Lie algebra
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simpleLieAlgebra(String,ZZ) -- construct a simple Lie algebra
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simpleRoots -- returns the simple roots of a simple Lie algebra
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simpleRoots(LieAlgebra) -- returns the simple roots of a simple Lie algebra
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simpleRoots(String,ZZ) -- returns the simple roots of a simple Lie algebra
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starInvolution -- computes w* for a weight w
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starInvolution(LieAlgebraModule) -- computes w* for a weight w
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subLieAlgebra -- Define a sub-Lie algebra of an existing one
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subLieAlgebra(LieAlgebra,List) -- Define a sub-Lie algebra of an existing one
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subLieAlgebra(LieAlgebra,Matrix) -- Define a sub-Lie algebra of an existing one
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symmetricPower(ZZ,LieAlgebraModule) -- Computes the nth symmetric / exterior tensor power of a Lie algebra module
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tensorCoefficient -- computes the multiplicity of W in U tensor V
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tensorCoefficient(LieAlgebraModule,LieAlgebraModule,LieAlgebraModule) -- computes the multiplicity of W in U tensor V
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trivialModule -- The trivial module of a Lie algebra
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trivialModule(LieAlgebra) -- The trivial module of a Lie algebra
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weightDiagram -- computes the weights in a Lie algebra module and their multiplicities
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weightDiagram(...,Strategy=>...) -- computes the weights in a Lie algebra module and their multiplicities
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weightDiagram(LieAlgebra,List) -- computes the weights in a Lie algebra module and their multiplicities
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weightDiagram(LieAlgebra,Vector) -- computes the weights in a Lie algebra module and their multiplicities
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weightDiagram(LieAlgebraModule) -- computes the weights in a Lie algebra module and their multiplicities
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weylAlcove -- the dominant integral weights of level less than or equal to l
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weylAlcove(LieAlgebra,ZZ) -- the dominant integral weights of level less than or equal to l
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weylAlcove(String,ZZ,ZZ) -- the dominant integral weights of level less than or equal to l
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weylAlcove(ZZ,LieAlgebra) -- the dominant integral weights of level less than or equal to l