48.38 SortCharactersCharTable

SortCharactersCharTable( tbl )
SortCharactersCharTable( tbl, permutation )
SortCharactersCharTable( tbl, chars )
SortCharactersCharTable( tbl, chars, permutation )
SortCharactersCharTable( tbl, chars, "norm" )
SortCharactersCharTable( tbl, chars, "degree" )

If no list chars of characters of the character table tbl is entered, SortCharactersCharTable sorts tbl.irreducibles; then additionally the list tbl.irredinfo is permuted by the same permutation. Otherwise SortCharactersCharTable sorts the list chars.

There are four possibilities to sort characters: Besides the application of an explicitly given permutation (see Permuted), they can be sorted according to ascending norms (parameter "norm"), to ascending degree (parameter "degree") or both (no third parameter), i.e., characters with same norm are sorted according to ascending degree, and characters with smaller norm precede those with bigger norm.

If the trivial character is contained in the sorted list, it will be sorted to the first position. Rational characters always will precede other ones with same norm resp. same degree afterwards.

SortCharactersCharTable returns the permutation that was applied to chars.

    gap> t:= CharTable( "Symmetric", 5 );;
    gap> PrintCharTable( t );
    rec( identifier := "S5", name := "S5", size := 120, order :=
    120, centralizers := [ 120, 12, 8, 6, 6, 4, 5 ], orders :=
    [ 1, 2, 2, 3, 6, 4, 5 ], powermap :=
    [ , [ 1, 1, 1, 4, 4, 3, 7 ], [ 1, 2, 3, 1, 2, 6, 7 ],,
      [ 1, 2, 3, 4, 5, 6, 1 ] ], irreducibles :=
    [ [ 1, -1, 1, 1, -1, -1, 1 ], [ 4, -2, 0, 1, 1, 0, -1 ],
      [ 5, -1, 1, -1, -1, 1, 0 ], [ 6, 0, -2, 0, 0, 0, 1 ],
      [ 5, 1, 1, -1, 1, -1, 0 ], [ 4, 2, 0, 1, -1, 0, -1 ],
      [ 1, 1, 1, 1, 1, 1, 1 ] ], classparam :=
    [ [ 1, [ 1, 1, 1, 1, 1 ] ], [ 1, [ 2, 1, 1, 1 ] ], [ 1, [ 2, 2, 1 ] ],
      [ 1, [ 3, 1, 1 ] ], [ 1, [ 3, 2 ] ], [ 1, [ 4, 1 ] ], [ 1, [ 5 ] ]
     ], irredinfo := [ rec(
          charparam := [ 1, [ 1, 1, 1, 1, 1 ] ] ), rec(
          charparam := [ 1, [ 2, 1, 1, 1 ] ] ), rec(
          charparam := [ 1, [ 2, 2, 1 ] ] ), rec(
          charparam := [ 1, [ 3, 1, 1 ] ] ), rec(
          charparam := [ 1, [ 3, 2 ] ] ), rec(
          charparam := [ 1, [ 4, 1 ] ] ), rec(
          charparam := [ 1, [ 5 ] ] )
     ], text := "computed using generic character table for symmetric grou\
    ps", classes := [ 1, 10, 15, 20, 20, 30, 24
     ], operations := CharTableOps, fusions := [  ], fusionsource :=
    [  ], projections := [  ], projectionsource := [  ] )
    gap> SortCharactersCharTable( t, t.irreducibles, "norm" );
    (1,2,3,4,5,6,7)      # sort the trivial character to the first position
    gap> SortCharactersCharTable( t );
    (4,5,7)
    gap> t.irreducibles;
    [ [ 1, 1, 1, 1, 1, 1, 1 ], [ 1, -1, 1, 1, -1, -1, 1 ],
      [ 4, -2, 0, 1, 1, 0, -1 ], [ 4, 2, 0, 1, -1, 0, -1 ],
      [ 5, -1, 1, -1, -1, 1, 0 ], [ 5, 1, 1, -1, 1, -1, 0 ],
      [ 6, 0, -2, 0, 0, 0, 1 ] ]

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