48.37 DisplayCharTable

DisplayCharTable( tbl )
DisplayCharTable( tbl, arec )

DisplayCharTable prepares the data contained in the character table tbl for a pretty columnwise output.

In the first form DisplayCharTable prints all irreducible characters of the table tbl, together with the orders of the centralizers in factorized form and the available powermaps.

Thus it can be used to echo character tables in interactive use, being the value of the record field Print of a record field operations of tbl (see Character Table Records, Operations Records for Character Tables).

Each displayed character is given a name X.n.

The number of columns printed at one time depends on the actual linelength, which is restored by the function SizeScreen (see SizeScreen).

The first lines of the output describe the order of the centralizer of an element of the class factorized into its prime divisor.

The next line gives the name of the class. If the record field classnames of the table tbl is not bound, DisplayCharTable calls the function ClassNamesCharTable to determine the class names and to store them on the table tbl (see ClassNamesCharTable).

Preceded by a name Pn the next lines show the nth powermaps of tbl in terms of the former shown class names.

Every ambiguous or unknown (see Unknown) value of the table is displayed as a question mark ?.

Irrational character values are not printed explicitly because the lengths of their printed representation might disturb the view. Instead of that every irrational value is indicated by a name, which is a string of a least one capital letter.

Once a name for an irrational number is found, it is used all over the printed table. Moreover the complex conjugate and the star of an irrationality are represented by that very name preceded by a / resp. a *.

The printed character table is then followed by a legend, a list identifying the occurred symbols with their actual irrational value. Occasionally this identity is supplemented by a quadratic representation of the irrationality together with the corresponding ATLAS--notation.

    gap> a5:= CharTable("A5");;
    gap> DisplayCharTable(a5);
    A5

         2  2  2  .  .  .
         3  1  .  1  .  .
         5  1  .  .  1  1

           1a 2a 3a 5a 5b
        2P 1a 1a 3a 5b 5a
        3P 1a 2a 1a 5b 5a
        5P 1a 2a 3a 1a 1a

    X.1     1  1  1  1  1
    X.2     3 -1  .  A *A
    X.3     3 -1  . *A  A
    X.4     4  .  1 -1 -1
    X.5     5  1 -1  .  .

    A = -E(5)-E(5)^4
      = (1-ER(5))/2 = -b5

In the second form DisplayCharTable takes an argument record arec as an additional argument. This record can be used to change the default style for displaying a character as shown above. Its relevant fields are

chars:

an integer or a list of integers to select a sublist of the irreducible characters of tbl, or a list of characters of tbl (in this case the letter "X" is replaced by "Y"),

classes:

an integer or a list of integers to select a sublist of the classes of tbl,

centralizers:

suppresses the printing of the orders of the centralizers if false,

powermap:

an integer or a list of integers to select a subset of the available powermaps, or false to suppress the powermaps,

letter:

a single capital letter (e.~g. "P" for permutation characters) to replace "X",

indicator:

true enables the printing of the second Schur indicator, a list of integers enables the printing of the corresponding indicators.

    gap> arec:= rec( chars:= 4, classes:= [a5.3a..a5.5a],
    > centralizers:= false, indicator:= true, powermap:= [2] );;
    gap> Indicator( a5, 2 );;
    gap> DisplayCharTable( a5, arec );
    A5

              3a 5a
           2P 3a 5b
           2
    X.4    +   1 -1
    

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