[1m[4m[31m[1mQuaGroup[1m[4m[31m[0m Version 1.3 Willem A. de Graaf Willem A. de Graaf Email: [34mmailto: degraaf@science.unitn.it[0m Homepage: [34mhttp://www.science.unitn.it/~degraaf[0m ------------------------------------------------------- [1m[4m[31mCopyright[0m (C) 2002 Willem A. de Graaf ------------------------------------------------------- [1m[4m[31mContent (quagroup)[0m 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 -------------------------------------------------------