GAP Manual: 63.14. WeylCosetPermRepresentation

WeylCosetPermRepresentation( W, J )

returns the list of permutations induced by the standard generators of the Weyl group W on the cosets of the parabolic subgroup generated by the elements in the set J. The cosets are in the order determined by the result of the function WeylRightCosetRepresentatives( W, [1..W.dim], J )

    gap> W := Weyl( CartanMat("F",4) );;
    gap> WeylCosetPermRepresentation( W, [1,2,3] );
    #I  Number of cosets = 24
    [ ( 4, 5)( 6, 7)( 8,10)(16,18)(17,19)(20,21),
      ( 3, 4)( 7, 9)(10,12)(14,16)(15,17)(21,22),
      ( 2, 3)( 4, 6)( 5, 7)( 9,11)(12,14)(13,15)(17,20)(19,21)(22,23),
      ( 1, 2)( 6, 8)( 7,10)( 9,12)(11,13)(14,15)(16,17)(18,19)(23,24) ]

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