ON DOUBLE COSETS WITH THE TRIVIAL INTERSECTION PROPERTY AND KAZHDAN-LUSZTIG CELLS IN S-n

For a composition lambda of n our aim is to obtain reduced forms for all the elements in the Kazhdan-Lusztig (right) cell containing w(J(lambda)), the longest element of the standard parabolic subgroup of S-n corresponding to lambda. We investigate how far this is possible to achieve by looking at elements of the form w(J(lambda))d, where d is a prefix of an element of minimum length in a (W-J(lambda), B) double coset with the trivial intersection property, B being a parabolic subgroup of S-n whose type is 'dual' to that of W-J(lambda).