84.5 ChevieClassInfo for Coxeter cosets

ChevieClassInfo( WF )

returns information about the conjugacy classes of the Coxeter coset WF. The result is a record with three components: classtext contains a list of reduced words for the representatives in ConjugacyClasses(WF), classnames contains corresponding names for the classes, and classparams gives corresponding parameters for the classes. Let W be the Coxeter group CoxeterGroup(WF). In the case where -1notin W, i.e., phi=-w_0, they are obtained by multiplying by w_0 a set of representatives of it maximal length of the classes of W.

    gap> W := CoxeterGroup( "D", 4 );;
    gap> ChevieClassInfo( CoxeterCoset( W, (1,2,4) ) );
    rec(
      classtext := [ [ 1 ], [  ], [ 1, 2, 3, 1, 2, 3 ], [ 3 ], [ 1, 3 ], 
          [ 1, 2, 3, 1, 2, 4, 3, 2 ], [ 1, 2, 3, 2 ] ],
      classparams := 
       [ [ "C_3" ], [ "~A_2" ], [ "C_3+A_1" ], [ "~A_2+A_1" ], [ "F_4" ], 
          [ "~A_2+A_2" ], [ "F_4(a_1)" ] ],
      classnames := 
       [ "C_3", "~A_2", "C_3+A_1", "~A_2+A_1", "F_4", "~A_2+A_2", 
          "F_4(a_1)" ] ) 

This function requires the package "chevie" (see RequirePackage).

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