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CharacterTable -- the class of character tables

Description

This type represents the character table of a symmetric group. It is implemented as a hash table that stores the list of partitions, the size of the table and a matrix which stores the values of the table.

i1 : charTable = characterTable 5

o1 = | 1  1  1  1  1  1  1 |
     | -1 0  -1 1  0  2  4 |
     | 0  -1 1  -1 1  1  5 |
     | 1  0  0  0  -2 0  6 |
     | 0  1  -1 -1 1  -1 5 |
     | -1 0  1  1  0  -2 4 |
     | 1  -1 -1 1  1  -1 1 |

o1 : CharacterTable
 
i2 : a = new Partition from {3,1,1}; b = new Partition from {1,1,1,1,1}

o3 = Partition{1, 1, 1, 1, 1}

o3 : Partition
 
i4 : peek charTable

o4 = CharacterTable{degree => 5                                      }
                    index => HashTable{Partition{1, 1, 1, 1, 1} => 6}
                                       Partition{2, 1, 1, 1} => 5
                                       Partition{2, 2, 1} => 4
                                       Partition{3, 1, 1} => 3
                                       Partition{3, 2} => 2
                                       Partition{4, 1} => 1
                                       Partition{5} => 0
                    length => 7
                    values => | 1  1  1  1  1  1  1 |
                              | -1 0  -1 1  0  2  4 |
                              | 0  -1 1  -1 1  1  5 |
                              | 1  0  0  0  -2 0  6 |
                              | 0  1  -1 -1 1  -1 5 |
                              | -1 0  1  1  0  -2 4 |
                              | 1  -1 -1 1  1  -1 1 |

See also

Functions and methods returning an object of class CharacterTable:

  • characterTable -- returns the character table of the symmetric group

Methods that use an object of class CharacterTable:

For the programmer

The object CharacterTable is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in SpechtModule.m2:3305:0.