On double cosets with the trivial intersection property and kazhdan-lusztig cells in Sn

Abstract

For a composition λ of n our aim is to obtain reduced forms for all the elements in the Kazhdan-Lusztig (right) cell containing wJ(λ), the longest element of the standard parabolic subgroup of Sn corresponding to λ. We investigate how far this is possible to achieve by looking at elements of the form wJ(λ)d, where d is a prefix of an element of minimum length in a (WJ(λ), B) double coset with the trivial intersection property, B being a parabolic subgroup of Sn whose type is ‘dual’ to that of WJ(λ). © 2015 University of Isfahan.