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 ‎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)}‎.

Keywords:

symmetric group , Hecke algebra , Kazhdan-Lusztig cell , generalized tableau , parabolic subgroup