  
  
                                  [1X RepnDecomp [101X
  
  
         [1X Decompose representations of finite groups into irreducibles [101X
  
  
                                     1.2.1
  
  
                                  2 March 2022
  
  
                               Kaashif Hymabaccus
  
  
  
  Kaashif Hymabaccus
      Email:    [7Xmailto:kaashif@kaashif.co.uk[107X
      Homepage: [7Xhttps://kaashif.co.uk[107X
  
  -------------------------------------------------------
  
  
  [1XContents (RepnDecomp)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YGetting started with RepnDecomp[133X
      1.1-1 [33X[0;0YInstallation[133X
      1.1-2 [33X[0;0YNote on what is meant by a representation[133X
      1.1-3 [33X[0;0YAPI Overview[133X
  2 [33X[0;0YIsomorphisms between representations[133X
    2.1 [33X[0;0YFinding explicit isomorphisms[133X
      2.1-1 LinearRepresentationIsomorphism
      2.1-2 LinearRepresentationIsomorphismSlow
    2.2 [33X[0;0YTesting isomorphisms[133X
      2.2-1 AreRepsIsomorphic
      2.2-2 IsLinearRepresentationIsomorphism
  3 [33X[0;0YAlgorithms for unitary representations[133X
    3.1 [33X[0;0YUnitarising representations[133X
      3.1-1 UnitaryRepresentation
      3.1-2 IsUnitaryRepresentation
      3.1-3 LDLDecomposition
    3.2 [33X[0;0YDecomposing unitary representations[133X
      3.2-1 IrreducibleDecompositionDixon
  4 [33X[0;0YMiscellaneous useful functions[133X
    4.1 [33X[0;0YPredicates for representations[133X
      4.1-1 IsFiniteGroupLinearRepresentation
      4.1-2 IsFiniteGroupPermutationRepresentation
    4.2 [33X[0;0YEfficient summing over groups[133X
      4.2-1 GroupSumBSGS
    4.3 [33X[0;0YSpace-efficient representation of tensors of matrices[133X
      4.3-1 IsTensorProductOfMatricesObj
      4.3-2 IsTensorProductPairRep
      4.3-3 IsTensorProductKroneckerRep
      4.3-4 TensorProductOfMatrices
      4.3-5 CharacterOfTensorProductOfRepresentations
    4.4 [33X[0;0YMatrices and homomorphisms[133X
      4.4-1 ComposeHomFunction
    4.5 [33X[0;0YRepresentation theoretic functions[133X
      4.5-1 TensorProductRepLists
      4.5-2 DirectSumOfRepresentations
      4.5-3 DegreeOfRepresentation
      4.5-4 PermToLinearRep
      4.5-5 IsOrthonormalSet
  5 [33X[0;0YComputing decompositions of representations[133X
    5.1 [33X[0;0YBlock diagonalizing[133X
      5.1-1 BlockDiagonalBasisOfRepresentation
      5.1-2 BlockDiagonalRepresentation
    5.2 [33X[0;0YAlgorithms due to the authors[133X
      5.2-1 REPN_ComputeUsingMyMethod
      5.2-2 REPN_ComputeUsingMyMethodCanonical
    5.3 [33X[0;0YAlgorithms due to Serre[133X
      5.3-1 CanonicalDecomposition
      5.3-2 IrreducibleDecomposition
      5.3-3 IrreducibleDecompositionCollected
      5.3-4 REPN_ComputeUsingSerre
  6 [33X[0;0YCentralizer (commutant) rings[133X
    6.1 [33X[0;0YFinding a basis for the centralizer[133X
      6.1-1 CentralizerBlocksOfRepresentation
      6.1-2 CentralizerOfRepresentation
    6.2 [33X[0;0YUsing the centralizer for computations[133X
      6.2-1 ClassSumCentralizer
      6.2-2 ClassSumCentralizerNC
  
  
  [32X
