@article {
author = {McDonough, Thomas P. and Pallikaros, Christos A.},
title = {On double cosets with the trivial intersection property and Kazhdan-Lusztig cells in $S_n$},
journal = {International Journal of Group Theory},
volume = {4},
number = {2},
pages = {25-48},
year = {2015},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2015.9795},
abstract = {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},
url = {https://ijgt.ui.ac.ir/article_9795.html},
eprint = {https://ijgt.ui.ac.ir/article_9795_baa13d009c9d26331351ea54f83b545d.pdf}
}