78.5 PermCosetsSubgroup

PermCosetsSubgroup( W, H )

returns the list of permutations induced by the standard generators of the Coxeter group W on the cosets of the Coxeter subgroup H. The cosets are in the order determined by the result of the function ReducedRightCosetRepresentatives( W, H ).

    gap> W := CoxeterGroup( "F", 4 );;
    gap> PermCosetsSubgroup( W, ReflectionSubgroup( W, [ 1, 2, 3 ] ) );
    [ ( 4, 5)( 6, 7)( 8,10)(16,18)(17,20)(19,21), 
      ( 3, 4)( 7, 9)(10,12)(14,16)(15,17)(21,22), 
      ( 2, 3)( 4, 6)( 5, 7)( 9,11)(12,14)(13,15)(17,19)(20,21)(22,23), 
      ( 1, 2)( 6, 8)( 7,10)( 9,12)(11,13)(14,15)(16,17)(18,20)(23,24) ] 

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

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