QuaGroup
  
  
                                  Version 1.3
  
  
                               Willem A. de Graaf
  
  
  
  Willem A. de Graaf
      Email:    mailto: degraaf@science.unitn.it
      Homepage: http://www.science.unitn.it/~degraaf
  
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  Copyright
  (C) 2002 Willem A. de Graaf
  
  
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  Content (quagroup)
  
  1. Introduction
  2. Background
    2.1 Gaussian Binomials
    2.2 Quantized enveloping algebras
    2.3 Representations of $U_q(\mathfrak{g})$
    2.4 PBW-type bases
    2.5 The ${\mathbb Z}$-form of $U_q(\mathfrak{g})$
    2.6 The canonical basis
    2.7 The path model
    2.8 Notes
  3. QuaGroup
    3.1 Global constants
      3.1-1 QuantumField
      3.1-2 _q
    3.2 Gaussian integers
      3.2-1 GaussNumber
      3.2-2 GaussianFactorial
      3.2-3 GaussianBinomial
    3.3 Roots and root systems
      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 Weyl groups and their elements
      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 Quantized enveloping algebras
      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 Homomorphisms and automorphisms
      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 Hopf algebra structure
      3.7-1 TensorPower
      3.7-2 UseTwistedHopfStructure
      3.7-3 ComultiplicationMap
      3.7-4 AntipodeMap
      3.7-5 CounitMap
    3.8 Modules
      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 The path model
      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 Canonical bases
      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 Universal enveloping algebras
      3.11-1 UEA
      3.11-2 UnderlyingLieAlgebra
      3.11-3 HighestWeightModule
      3.11-4 QUEAToUEAMap
  
  
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