GAP Manual: 63.7. PermWeylWord

PermWeylWord( W , w )

returns the permutation on the root vectors determined by an element which is given as a list w of integers representing the standard generators of the Weyl group W.

    gap> W := Weyl( CartanMat("G",2) );;
    gap> PermWeylWord( W, [1,2,1] );
    ( 1,12)( 2, 4)( 3, 9)( 6, 7)( 8,10)

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