76.13 CoxeterConjugacyClasses

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).

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GAP 3.4.4
April 1997