76.14 ChevieClassInfo

ChevieClassInfo( W )

returns information about the conjugacy classes of the finite Coxeter group W. The result is a record with three components: classtext contains CoxeterConjugacyClass(W), classnames contains corresponding names for the classes, and classparams gives Character tables for Coxeter groups).

    gap> W := CoxeterGroup( "D", 4 );;
    gap> ChevieClassInfo( W );
    rec(
      classtext := 
       [ [  ], [ 1, 2 ], [ 1, 2, 3, 1, 2, 3, 4, 3, 1, 2, 3, 4 ], [ 1 ], 
          [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 4 ], [ 2, 4 ], 
          [ 1, 3, 1, 2, 3, 4 ], [ 1, 3 ], [ 1, 2, 3, 4 ], [ 1, 3, 4 ], 
          [ 2, 3, 4 ] ],
      classparams := 
       [ [ [ [ 1, 1, 1, 1 ], [  ] ] ], [ [ [ 1, 1 ], [ 1, 1 ] ] ], 
          [ [ [  ], [ 1, 1, 1, 1 ] ] ], [ [ [ 2, 1, 1 ], [  ] ] ], 
          [ [ [ 1 ], [ 2, 1 ] ] ], [ [ [ 2 ], [ 1, 1 ] ] ], 
          [ [ [ 2, 2 ], '+' ] ], [ [ [ 2, 2 ], '-' ] ], 
          [ [ [  ], [ 2, 2 ] ] ], [ [ [ 3, 1 ], [  ] ] ], 
          [ [ [  ], [ 3, 1 ] ] ], [ [ [ 4 ], '+' ] ], [ [ [ 4 ], '-' ] ] ]
       ,
      classnames := [ "1111.", "11.11", ".1111", "211.", "1.21", "2.11", 
          "22.+", "22.-", ".22", "31.", ".31", "4.+", "4.-" ] )

For a general description of the conjugacy classes in the Weyl groups, see Car72. The relevance of taking representatives of minimal length is explained in GP93.