  
  
                                   [1X QuaGroup [101X
  
  
                       [1X Computations with quantum groups [101X
  
  
                                 Version 1.8.4
  
  
                                11 January 2024
  
  
                            Willem Adriaan de Graaf
  
  
  
  Willem Adriaan de Graaf
      Email:    [7Xmailto:degraaf@science.unitn.it[107X
      Homepage: [7Xhttp://www.science.unitn.it/~degraaf[107X
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2002 Willem A. de Graaf[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (quagroup)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YBackground[133X
    2.1 [33X[0;0YGaussian Binomials[133X
    2.2 [33X[0;0YQuantized enveloping algebras[133X
    2.3 [33X[0;0YRepresentations of [23XU_q(\mathfrak{g})[123X[133X
    2.4 [33X[0;0YPBW-type bases[133X
    2.5 [33X[0;0YThe [23X{\mathbb Z}[123X-form of [23XU_q(\mathfrak{g})[123X[133X
    2.6 [33X[0;0YThe canonical basis[133X
    2.7 [33X[0;0YThe path model[133X
    2.8 [33X[0;0YNotes[133X
  3 [33X[0;0YQuaGroup[133X
    3.1 [33X[0;0YGlobal constants[133X
      3.1-1 QuantumField
      3.1-2 _q
    3.2 [33X[0;0YGaussian integers[133X
      3.2-1 GaussNumber
      3.2-2 GaussianFactorial
      3.2-3 GaussianBinomial
    3.3 [33X[0;0YRoots and root systems[133X
      3.3-1 RootSystem
      3.3-2 BilinearFormMatNF
      3.3-3 PositiveRootsNF
      3.3-4 SimpleSystemNF
      3.3-5 PositiveRootsInConvexOrder
      3.3-6 SimpleRootsAsWeights
    3.4 [33X[0;0YWeyl groups and their elements[133X
      3.4-1 ApplyWeylElement
      3.4-2 LengthOfWeylWord
      3.4-3 LongestWeylWord
      3.4-4 ReducedWordIterator
      3.4-5 ExchangeElement
      3.4-6 GetBraidRelations
      3.4-7 LongWords
    3.5 [33X[0;0YQuantized enveloping algebras[133X
      3.5-1 QuantizedUEA
      3.5-2 ObjByExtRep
      3.5-3 ExtRepOfObj
      3.5-4 QuantumParameter
      3.5-5 CanonicalMapping
      3.5-6 WriteQEAToFile
      3.5-7 ReadQEAFromFile
    3.6 [33X[0;0YHomomorphisms and automorphisms[133X
      3.6-1 QEAHomomorphism
      3.6-2 QEAAutomorphism
      3.6-3 QEAAntiAutomorphism
      3.6-4 AutomorphismOmega
      3.6-5 AntiAutomorphismTau
      3.6-6 BarAutomorphism
      3.6-7 AutomorphismTalpha
      3.6-8 DiagramAutomorphism
      3.6-9 \*
    3.7 [33X[0;0YHopf algebra structure[133X
      3.7-1 TensorPower
      3.7-2 UseTwistedHopfStructure
      3.7-3 ComultiplicationMap
      3.7-4 AntipodeMap
      3.7-5 CounitMap
    3.8 [33X[0;0YModules[133X
      3.8-1 HighestWeightModule
      3.8-2 IrreducibleQuotient
      3.8-3 HWModuleByTensorProduct
      3.8-4 DIYModule
      3.8-5 TensorProductOfAlgebraModules
      3.8-6 HWModuleByGenerator
      3.8-7 InducedQEAModule
      3.8-8 GenericModule
      3.8-9 CanonicalMapping
      3.8-10 U2Module
      3.8-11 MinusculeModule
      3.8-12 DualAlgebraModule
      3.8-13 TrivialAlgebraModule
      3.8-14 WeightsAndVectors
      3.8-15 HighestWeightsAndVectors
      3.8-16 RMatrix
      3.8-17 IsomorphismOfTensorModules
      3.8-18 WriteModuleToFile
      3.8-19 ReadModuleFromFile
    3.9 [33X[0;0YThe path model[133X
      3.9-1 DominantLSPath
      3.9-2 Falpha
      3.9-3 Ealpha
      3.9-4 LSSequence
      3.9-5 WeylWord
      3.9-6 EndWeight
      3.9-7 CrystalGraph
    3.10 [33X[0;0YCanonical bases[133X
      3.10-1 Falpha
      3.10-2 Ealpha
      3.10-3 CanonicalBasis
      3.10-4 PBWElements
      3.10-5 MonomialElements
      3.10-6 Strings
      3.10-7 PrincipalMonomial
      3.10-8 StringMonomial
      3.10-9 Falpha
      3.10-10 Ealpha
      3.10-11 CrystalBasis
      3.10-12 CrystalVectors
      3.10-13 Falpha
      3.10-14 Ealpha
      3.10-15 CrystalGraph
    3.11 [33X[0;0YUniversal enveloping algebras[133X
      3.11-1 UEA
      3.11-2 UnderlyingLieAlgebra
      3.11-3 HighestWeightModule
      3.11-4 QUEAToUEAMap
  
  
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