2021/09/28 by Zhekun He, Jun Hu, He, Zhekun +3
Mathematics · #16G99 #20C08 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16G99 #msc:20C08
paper · pdf · doi:10.48550/arxiv.2109.13646
arxiv created 2021/09/28 · openalex publication_date 2021/09/28 · arxiv updated 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let "≤L" be the Kazhdan-Lusztig left cell preorder on the symmetric group Sn. Let w↦ (P(w),Q(w)) be the Robinson-Schensted-Knuth correspondence between Sn and the set of standard tableaux with the same shapes. We prove that for any x,y∈ Sn, x≤L y only if Q(y)\unrhd Q(x), where "\unrhd" is the dominance (partial) order between standard tableaux. As a byproduct, we generalize an earlier result of Geck by showing that each Kazhdan-Lusztig basis element C'w can be expressed as a linear combination of some muv which satisfies that u\unrhd P(w)^*, v\unrhd Q(w)^*, where t^* denotes the conjugate of t for each standard tableau t, \mst | s,t∈ Std(λ),λ\vdash n\ is the Murphy basis of the Iwahori-Hecke algebra Hv(Sn) associated to Sn.