77.1 CharTable for Coxeter groups

CharTable( W )

returns the character table of the Coxeter group W. This is a character table record as defined in GAP. It is assigned to the record component charTable of W. The function CharTable checks if this component is already bound. The (variable) record components classtext, classnames and irredinfo contain the following information.

classtext:

a list of reduced expressions for minimal length representatives in the conjugacy classes of W

classnames:

a list of Carter's admissible diagrams (for exceptional, irreducible types) or partitions resp. pairs of partitions (for classical, irreducible types). If the Coxeter group is not irreducible tuples of such labels are given.

irredinfo:

a list of records with a component charname which contains a string with a label for an irreducible character. For an irreducible Coxeter group this label can either be a partition or a pair of partitions, or it is a pair (n,e) where n is the degree of the character and e is the smallest symmetric power of the character of the natural reflection representation which contains the given character as a component. The optional second component, charparam, contains this label as a list of numbers (if it is possible to give it in this way). The labels for the group is a list of labels corresponding to the irreducible components (as given by CartanType).

    gap> W := CoxeterGroup( "G", 2);;
    gap> ct := CharTable( W );
    CharTable( "W( G2 )" )
    gap> ct.classtext;
    [ [  ], [ 2 ], [ 1 ], [ 1, 2 ], [ 1, 2, 1, 2 ], [ 1, 2, 1, 2, 1, 2 ] ]
    gap> ct.classnames;
    [ " ", "~A_1", "A_1", "G_2", "A_2", "A_1 + ~A_1" ]
    gap> ct.irredinfo;
    [ rec(
          charparam := [ [ 1, 0 ] ],
          charname := "phi_{1,0}" ), rec(
          charparam := [ [ 1, 6 ] ],
          charname := "phi_{1,6}" ), rec(
          charparam := [ [ 1, 3, "'" ] ],
          charname := "phi_{1,3}'" ), rec(
          charparam := [ [ 1, 3, "''" ] ],
          charname := "phi_{1,3}''" ), rec(
          charparam := [ [ 2, 1 ] ],
          charname := "phi_{2,1}" ), rec(
          charparam := [ [ 2, 2 ] ],
          charname := "phi_{2,2}" ) ] 

These functions require the package "chevie" (see RequirePackage). Up Top Next
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