2015/03/02 by Van Minh Nguyen, Nguyen, Van Minh
Mathematics · #20C08 #20C30 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C08 #msc:20C30
paper · pdf · doi:10.48550/arxiv.1503.00409
12 pages
openalex publication_date 2015/03/02 · arxiv created 2015/03/04 · arxiv updated 2015/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (W,S) be a Coxeter system of type A, so that W can be identified with the symmetric group Sym(n) for some positive integer n and S with the set of simple transpositions \ (i,i+1)| 1\leqslant i\leqslant n-1 \. Let \leqslant\mathsf L denote the left weak order on W, and for each J⊆ S let wJ be the longest element of the subgroup WJ generated by J. We show that the basic skew diagrams with n boxes are in bijective correspondence with the pairs (w,J) such that the set \ x∈ W| wJ\leqslant\mathsf L x\leqslant\mathsf L wwJ \ is a nonempty union of Kazhdan-Lusztig left cells. These are also the pairs (w,J) such that \mathscrI(w)=\ v∈ W| v\leqslant\mathsf L w \ is a W -graph ideal with respect to J. Moreover, for each such pair the elements of \mathscrI(w) are in bijective correspondence with the standard tableaux associated with the corresponding skew diagram.