On embedding certain Kazhdan-Lusztig cells of Sn into cells of Sn+1

T. P. McDonough, C. A. Pallikaros

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)

Abstract

In this paper, we consider a particular class of Kazhdan–Lusztig cells in the symmetric group S n, the cells containing involutions associated with compositions λ of n. For certain families of compositions we are able to give an explicit description of the corresponding cells by obtaining reduced forms for all their elements. This is achieved by first finding a particular class of diagrams E ( λ ) which lead to a subset of the cell from which the remaining elements of the cell are easily obtained. Moreover, we show that for certain cases of related compositions λ and λ^ of n and n+ 1 respectively, the members of E ( λ ) and E ( λ^ ) are also related in an analogous way. This allows us to associate certain cells in S n with cells in S n + 1 in a well-defined way, which is connected to the induction and restriction of cells.

Original languageEnglish
Pages (from-to)523-547
Number of pages25
JournalBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Volume59
Issue number3
Early online date30 Dec 2017
DOIs
Publication statusPublished - 01 Sept 2018

Keywords

  • Induction and restriction
  • Kazhdan–Lusztig cell
  • Symmetric group

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