CoxeterConjugacyClasses( W )
returns a list of representatives of the conjugacy classes of the Coxeter group W. Each element in this list is given as a word in the standard generators, where the generator s_i is represented by the number i in a list. Each representative has the property that it is of minimal length in its conjugacy class.
gap> CoxeterConjugacyClasses( CoxeterGroup( "F", 4 ) ); [ [ ], [ 1, 2, 1, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3, 4 ], [ 2, 3, 2, 3 ], [ 2, 1 ], [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ], [ 3, 2, 4, 3, 2, 1, 3, 2, 4, 3, 2, 1 ], [ 4, 3 ], [ 1, 2, 1, 4, 3, 2, 1, 3, 2, 3 ], [ 3, 2, 1, 4, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2 ], [ 3, 2, 4, 3, 2, 1, 3, 2 ], [ 4, 3, 2, 1 ], [ 1 ], [ 2, 3, 2, 3, 4, 3, 2, 3, 4 ], [ 1, 4, 3 ], [ 4, 3, 2 ], [ 2, 3, 2, 1, 3 ], [ 3 ], [ 1, 2, 1, 3, 2, 1, 3, 2, 3 ], [ 2, 1, 4 ], [ 3, 2, 1 ], [ 2, 4, 3, 2, 3 ], [ 1, 3 ], [ 3, 2 ], [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 2, 4, 3, 2, 1 ], [ 2, 4, 3, 2, 1, 3 ] ]See also ChevieClassInfo.
This function requires the package "chevie" (see RequirePackage).
GAP 3.4.4