83.5 LeftCells

LeftCells( W )

returns a list of pairs. The first component of each pair consists of the reduced words in the Coxeter group W which lie in one left cell C, the second component consists of the corresponding matrix of highest coefficients mu_{y,w}, where y,w are in C.

    gap> W := CoxeterGroup( "G", 2 );;
    gap> LeftCells(W);
    [ [ [ [  ] ], [ [ 0 ] ] ], 
      [ [ [ 1 ], [ 2, 1 ], [ 1, 2, 1 ], [ 2, 1, 2, 1 ], [ 1, 2, 1, 2, 1 ] 
             ], 
          [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 1, 0, 0 ], [ 0, 1, 0, 1, 0 ], 
              [ 0, 0, 1, 0, 1 ], [ 0, 0, 0, 1, 0 ] ] ], 
      [ [ [ 1, 2, 1, 2, 1, 2 ] ], [ [ 0 ] ] ], 
      [ [ [ 2 ], [ 1, 2 ], [ 2, 1, 2 ], [ 1, 2, 1, 2 ], [ 2, 1, 2, 1, 2 ] 
             ], 
          [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 1, 0, 0 ], [ 0, 1, 0, 1, 0 ], 
              [ 0, 0, 1, 0, 1 ], [ 0, 0, 0, 1, 0 ] ] ] ] 

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

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