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The GAP Character Table Library

(Version 1.2.1)

Thomas Breuer
Email: [email protected]
Homepage: http://www.math.rwth-aachen.de/~Thomas.Breuer

Copyright

© 2003–2012

This package may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see http://www.gnu.org/licenses.

Contents

1 Introduction to the GAP Character Table Library

1.1 History of the GAP Character Table Library

1.2 What's New in CTblLib, Compared to Older Versions?

1.2-1 What's New in Version 1.2?
1.2-2 What's New in Version 1.1?

1.3 Acknowledgements

2 Tutorial for the GAP Character Table Library

2.1 Concepts used in the GAP Character Table Library

2.2 Accessing a Character Table from the Library

  2.2-1 Accessing a Character Table via a name
  2.2-2 Accessing a Character Table via properties
  2.2-3 Accessing a Character Table via a Table of Marks
  2.2-4 Accessing a Character Table relative to another Character Table
  2.2-5 Different character tables for the same group

2.3 Examples of Using the GAP Character Table Library

  2.3-1 Example: Ambivalent Simple Groups
  2.3-2 Example: Simple p-pure Groups
  2.3-3 Example: Simple Groups with only one p-Block
  2.3-4 Example:The Sylow 3 subgroup of 3.O'N
  2.3-5 Example: Primitive Permutation Characters of 2.A_6
  2.3-6 Example: A Permutation Character of Fi_23

3 The User Interface to the GAP Character Table Library

3.1 Accessing Data of the CTblLib Package

  3.1-1 Admissible Names for Character Tables in CTblLib
  3.1-2 CharacterTable
  3.1-3 AllCharacterTableNames
  3.1-4 OneCharacterTableName
  3.1-5 NameOfEquivalentLibraryCharacterTable

3.2 The Interface to the TomLib Package

  3.2-1 TableOfMarks
  3.2-2 CharacterTable
  3.2-3 FusionCharTableTom
  3.2-4 FusionToTom
  3.2-5 NameOfLibraryCharacterTable

3.3 The Interface to GAP's Group Libraries

  3.3-1 GroupInfoForCharacterTable
  3.3-2 KnowsSomeGroupInfo
  3.3-3 CharacterTableForGroupInfo
  3.3-4 GroupForGroupInfo
  3.3-5 GroupForTom
  3.3-6 AtlasStabilizer
  3.3-7 IsNontrivialDirectProduct

3.4 Unipotent Characters of Finite Groups of Lie Type

  3.4-1 UnipotentCharacter
  3.4-2 DeligneLusztigNames
  3.4-3 DeligneLusztigName
  3.4-4 KnowsDeligneLusztigNames

3.5 Browse Applications Provided by CTblLib

  3.5-1 DisplayCTblLibInfo
  3.5-2 BrowseCTblLibInfo
  3.5-3 BrowseCommonIrrationalities
  3.5-4 BrowseCTblLibDifferences

3.6 Duplicates of Library Character Tables

  3.6-1 IsDuplicateTable
  3.6-2 IdentifierOfMainTable
  3.6-3 IdentifiersOfDuplicateTables

3.7 Attributes for Library Character Tables

  3.7-1 Maxes
  3.7-2 ProjectivesInfo
  3.7-3 ExtensionInfoCharacterTable
  3.7-4 ConstructionInfoCharacterTable

4 Contents of the GAP Character Table Library

4.1 Ordinary and Brauer Tables in the GAP Character Table Library

4.1-1 Ordinary Character Tables
4.1-2 Brauer Tables

4.2 Generic Character Tables

  4.2-1 Available generic character tables
  4.2-2 CharacterTableSpecialized
  4.2-3 Components of generic character tables
  4.2-4 Example: The generic table of cyclic groups
  4.2-5 Example: The generic table of the general linear group GL(2,q)

4.3 Atlas Tables

  4.3-1 Improvements to the Atlas
  4.3-2 Power Maps
  4.3-3 Projective Characters and Projections
  4.3-4 Tables of Isoclinic Groups
  4.3-5 Ordering of Characters and Classes
  4.3-6 AtlasLabelsOfIrreducibles
  4.3-7 Examples of the Atlas Format for GAP Tables

4.4 CAS Tables

4.5 Customizations of the GAP Character Table Library

4.5-1 Installing the GAP Character Table Library
4.5-2 Unloading Character Table Data

4.6 Technicalities of the Access to Character Tables from the Library

  4.6-1 Data Files of the GAP Character Table Library
  4.6-2 LIBLIST
  4.6-3 LibInfoCharacterTable

4.7 How to Extend the GAP Character Table Library

  4.7-1 NotifyNameOfCharacterTable
  4.7-2 LibraryFusion
  4.7-3 PrintToLib
  4.7-4 NotifyCharacterTable

4.8 Sanity Checks for the GAP Character Table Library

4.9 Maintenance of the GAP Character Table Library

5 Functions for Character Table Constructions

5.1 Character Tables of Groups of Structure M.G.A

  5.1-1 PossibleCharacterTablesOfTypeMGA
  5.1-2 BrauerTableOfTypeMGA
  5.1-3 PossibleActionsForTypeMGA

5.2 Character Tables of Groups of Structure G.S_3

5.2-1 CharacterTableOfTypeGS3
5.2-2 PossibleActionsForTypeGS3

5.3 Character Tables of Groups of Structure G.2^2

5.3-1 PossibleCharacterTablesOfTypeGV4
5.3-2 PossibleActionsForTypeGV4

5.4 Character Tables of Groups of Structure 2^2.G

5.4-1 PossibleCharacterTablesOfTypeV4G
5.4-2 BrauerTableOfTypeV4G

5.5 Character Tables of Subdirect Products of Index Two

  5.5-1 CharacterTableOfIndexTwoSubdirectProduct
  5.5-2 ConstructIndexTwoSubdirectProduct
  5.5-3 ConstructIndexTwoSubdirectProductInfo

5.6 Brauer Tables of Extensions by p-regular Automorphisms

5.6-1 IBrOfExtensionBySingularAutomorphism

5.7 Character Tables of Coprime Central Extensions

5.7-1 CharacterTableOfCommonCentralExtension

5.8 Construction Functions used in the Character Table Library

  5.8-1 ConstructMGA
  5.8-2 ConstructMGAInfo
  5.8-3 ConstructGS3
  5.8-4 ConstructV4G
  5.8-5 ConstructProj
  5.8-6 ConstructDirectProduct
  5.8-7 ConstructCentralProduct
  5.8-8 ConstructSubdirect
  5.8-9 ConstructWreathSymmetric
  5.8-10 ConstructIsoclinic
  5.8-11 ConstructPermuted
  5.8-12 ConstructAdjusted
  5.8-13 ConstructFactor

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