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

Document Type : Ischia Group Theory 2014


1 Department of Mathematics, Aberystwyth University

2 Department of Mathematics and Statistics, University of Cyprus


‎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 $W_{J(\lambda)}$‎.


Main Subjects

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Volume 4, Issue 2 - Serial Number 2
Proceedings of the Ischia Group Theory 2014-Part II.
June 2015
Pages 25-48
  • Receive Date: 24 January 2015
  • Revise Date: 03 June 2015
  • Accept Date: 03 June 2015
  • Published Online: 01 June 2015