University of Isfahan International Journal of Group Theory 2251-7650 4 2 2015 06 01 On double cosets with the trivial intersection property and kazhdan-lusztig cells in Sn 25 48 9795 10.22108/ijgt.2015.9795 EN Thomas P. McDonough Department of Mathematics, Aberystwyth University Christos A. Pallikaros Department of Mathematics and Statistics, University of Cyprus Journal Article 2015 01 24 ‎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 $W_{J(\lambda)}$‎. https://ijgt.ui.ac.ir/article_9795_baa13d009c9d26331351ea54f83b545d.pdf