2017/07/21 by T. P. McDonough, McDonough, T. P., C. A. Pallikaros +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1707.06761
openalex publication_date 2017/07/21 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28
In this paper, we consider a particular class of Kazhdan-Lusztig cells in the symmetric group Sn, 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 Sn with cells in Sn+1 in a well-defined way, which is connected to the induction and restriction of cells.