  
  
                                    [1X hecke [101X
  
  
             [1X Calculating decomposition matrices of Hecke algebras [101X
  
  
                                     1.5.3
  
  
                                1 September 2019
  
  
                                Dmitriy Traytel
  
  
  
  Dmitriy Traytel
      Email:    [7Xmailto:traytel@in.tum.de[107X
      Homepage: [7Xhttp://home.in.tum.de/~traytel/hecke/[107X
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2010–2013 by Dmitriy Traytel[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2 or higher.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0Y[5XHecke[105X  is  a  port  of the [5XGAP[105X 3 package [5XSpecht[105X 2.4 to [5XGAP[105X 4. [5XSpecht[105X 2.4 was
  written by Andrew Mathas, who allowed Dmitriy Traytel to use his source code
  as the basis for [5Xhecke[105X.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (hecke)[101X
  
  1 [33X[0;0YDecomposition numbers of Hecke algebras of type A[133X
    1.1 [33X[0;0YDescription[133X
    1.2 [33X[0;0YThe modular representation theory of Hecke algebras[133X
    1.3 [33X[0;0YTwo small examples[133X
    1.4 [33X[0;0YOverview over this manual[133X
    1.5 [33X[0;0YCredits[133X
  2 [33X[0;0YInstallation of the [5Xhecke[105X-Package[133X
  3 [33X[0;0YSpecht functionality[133X
    3.1 [33X[0;0YPorting notes[133X
      3.1-1 [33X[0;0YStructure of [5XHecke[105X[133X
      3.1-2 [33X[0;0YRenamings[133X
    3.2 [33X[0;0YSpecht functions[133X
      3.2-1 Specht
      3.2-2 [33X[0;0YSimple information access[133X
      3.2-3 [33X[0;0YThe functions MakeSpecht, MakePIM and MakeSimple[133X
      3.2-4 [33X[0;0YDecomposition numbers of the symmetric groups[133X
      3.2-5 [33X[0;0YHecke algebras over fields of positive characteristic[133X
      3.2-6 [33X[0;0YThe Fock space and Hecke algebras over fields of characteristic
      zero[133X
      3.2-7 Schur
      3.2-8 DecompositionMatrix
      3.2-9 CrystalDecompositionMatrix
      3.2-10 DecompositionNumber
    3.3 [33X[0;0YPartitions in [5XHecke[105X[133X
    3.4 [33X[0;0YInducing and restricting modules[133X
      3.4-1 RInducedModule
      3.4-2 SInducedModule
      3.4-3 RRestrictedModule
      3.4-4 SRestrictedModule
    3.5 [33X[0;0YOperations on decomposition matrices[133X
      3.5-1 InducedDecompositionMatrix
      3.5-2 IsNewIndecomposable
      3.5-3 InvertDecompositionMatrix
      3.5-4 AdjustmentMatrix
      3.5-5 SaveDecompositionMatrix
      3.5-6 CalculateDecompositionMatrix
      3.5-7 MatrixDecompositionMatrix
      3.5-8 DecompositionMatrixMatrix
      3.5-9 AddIndecomposable
      3.5-10 RemoveIndecomposable
      3.5-11 MissingIndecomposables
    3.6 [33X[0;0YCalculating dimensions[133X
      3.6-1 SimpleDimension
      3.6-2 SpechtDimension
    3.7 [33X[0;0YCombinatorics on Young diagrams[133X
      3.7-1 Schaper
      3.7-2 IsSimpleModule
      3.7-3 MullineuxMap
      3.7-4 MullineuxSymbol
      3.7-5 PartitionMullineuxSymbol
      3.7-6 GoodNodes
      3.7-7 NormalNodes
      3.7-8 GoodNodeSequence
      3.7-9 PartitionGoodNodeSequence
      3.7-10 GoodNodeLatticePath
      3.7-11 LittlewoodRichardsonRule
      3.7-12 InverseLittlewoodRichardsonRule
      3.7-13 EResidueDiagram
      3.7-14 HookLengthDiagram
      3.7-15 RemoveRimHook
      3.7-16 AddRimHook
    3.8 [33X[0;0YOperations on partitions[133X
      3.8-1 ECore
      3.8-2 IsECore
      3.8-3 EQuotient
      3.8-4 CombineEQuotientECore
      3.8-5 EWeight
      3.8-6 ERegularPartitions
      3.8-7 IsERegular
      3.8-8 ConjugatePartition
      3.8-9 PartitionBetaSet
      3.8-10 ETopLadder
      3.8-11 Dominates
      3.8-12 LengthLexicographic
      3.8-13 Lexicographic
      3.8-14 ReverseDominance
    3.9 [33X[0;0YMiscellaneous functions on modules[133X
      3.9-1 Specialized
      3.9-2 ERegulars
      3.9-3 SplitECores
      3.9-4 Coefficient
      3.9-5 InnerProduct
    3.10 [33X[0;0YSemi-standard and standard tableaux[133X
      3.10-1 Tableau
      3.10-2 SemiStandardTableaux
      3.10-3 StandardTableaux
      3.10-4 ConjugateTableau
      3.10-5 ShapeTableau
      3.10-6 TypeTableau
  
  
  [32X
