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QuaGroup

Computations with quantum groups

Version 1.8.4

11 January 2024

Willem Adriaan de Graaf
Email: degraaf@science.unitn.it
Homepage: http://www.science.unitn.it/~degraaf

Copyright

© 2002 Willem A. de Graaf

Contents

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

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

3.9 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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