On double cosets with the trivial intersection property and kazhdan-lusztig cells in Sn
نویسندگان
1 Department of Mathematics, Aberystwyth University
2 Department of Mathematics and Statistics, University of Cyprus
doi
10.22108/ijgt.2015.9795چکیده
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 $W_{J(\lambda)}$.
