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

Thomas P. McDonough, Christos A. Pallikaros*

*Corresponding author for this work

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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).

Original languageEnglish
Pages (from-to)25-48
Number of pages24
JournalInternational Journal of Group Theory
Volume4
Issue number2
Publication statusPublished - 2015

Keywords

  • Generalized tableau
  • Hecke algebra
  • Kazhdan-Lusztig cell
  • Parabolic subgroup
  • Symmetric group

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