  
  
                                     [1X SLA [101X
  
  
                      [1X Computing with simple Lie algebras [101X
  
  
                                 Version 1.6.2
  
  
                                  12 July 2024
  
  
                            Willem Adriaan de Graaf
  
  
  
  Willem Adriaan de Graaf
      Email:    [7Xmailto:degraaf@science.unitn.it[107X
      Homepage: [7Xhttp://www.science.unitn.it/~degraaf[107X
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThis  package  provides  functions for computing with various aspects of the
  theory of simple Lie algebras in characteristic zero.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2013-2018 Willem de Graaf[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (SLA)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YRoot Systems and Weyl Groups[133X
    2.1 [33X[0;0YRoot Systems[133X
      2.1-1 ExtendedCartanMatrix
      2.1-2 CartanType
      2.1-3 DisplayDynkinDiagram
    2.2 [33X[0;0YWeyl groups[133X
      2.2-1 WeylTransversal
      2.2-2 SizeOfWeylGroup
      2.2-3 WeylGroupAsPermGroup
      2.2-4 ApplyWeylPermToWeight
      2.2-5 WeylWordAsPerm
      2.2-6 PermAsWeylWord
  3 [33X[0;0YSemisimple Lie Algebras and their Modules[133X
    3.1 [33X[0;0YSemisimple Lie algebras[133X
      3.1-1 IsomorphismOfSemisimpleLieAlgebras
      3.1-2 DisplayDynkinDiagram
      3.1-3 ApplyWeylPermToCartanElement
    3.2 [33X[0;0YRepresentations of semisimple Lie algebras[133X
      3.2-1 AdmissibleLattice
      3.2-2 DirectSumDecomposition
      3.2-3 IsIrreducibleHWModule
      3.2-4 HighestWeightVector
      3.2-5 HighestWeight
      3.2-6 DisplayHighestWeight
      3.2-7 IsomorphismOfIrreducibleHWModules
      3.2-8 DualAlgebraModule
      3.2-9 CharacteristicsOfStrata
  4 [33X[0;0YNilpotent Orbits[133X
    4.1 [33X[0;0YThe functions[133X
      4.1-1 NilpotentOrbit
      4.1-2 NilpotentOrbits
      4.1-3 WeightedDynkinDiagram
      4.1-4 WeightedDynkinDiagram
      4.1-5 DisplayWeightedDynkinDiagram
      4.1-6 DisplayWeightedDynkinDiagram
      4.1-7 AmbientLieAlgebra
      4.1-8 SemiSimpleType
      4.1-9 SL2Triple
      4.1-10 RandomSL2Triple
      4.1-11 SL2Grading
      4.1-12 SL2Triple
      4.1-13 Dimension
      4.1-14 IsRegular
      4.1-15 RegularNilpotentOrbit
      4.1-16 IsDistinguished
      4.1-17 DistinguishedNilpotentOrbits
      4.1-18 ComponentGroup
      4.1-19 InducedNilpotentOrbits
      4.1-20 RigidNilpotentOrbits
      4.1-21 RichardsonOrbits
  5 [33X[0;0YFinite Order Automorphisms and [22Xθ[122X-Groups[133X
    5.1 [33X[0;0YThe functions[133X
      5.1-1 FiniteOrderInnerAutomorphisms
      5.1-2 FiniteOrderOuterAutomorphisms
      5.1-3 Order
      5.1-4 KacDiagram
      5.1-5 Grading
      5.1-6 NilpotentOrbitsOfThetaRepresentation
      5.1-7 ClosureDiagram
      5.1-8 CarrierAlgebra
      5.1-9 CartanSubspace
  6 [33X[0;0YSemisimple Subalgebras of Semisimple Lie Algebras[133X
    6.1 [33X[0;0YBranching[133X
      6.1-1 ProjectionMatrix
      6.1-2 Branching
    6.2 [33X[0;0YConstructing Semisimple Subalgebras[133X
      6.2-1 RegularSemisimpleSubalgebras
      6.2-2 SSSTypes
      6.2-3 LieAlgebraAndSubalgebras
      6.2-4 InclusionsGraph
      6.2-5 SubalgebrasInclusion
      6.2-6 DynkinIndex
      6.2-7 AreLinearlyEquivalentSubalgebras
      6.2-8 MakeDatabaseEntry
      6.2-9 ClosedSubsets
      6.2-10 DecompositionOfClosedSet
      6.2-11 IsSpecialClosedSet
      6.2-12 LieAlgebraOfClosedSet
  
  
  [32X
