Two formulae for inverse Kazhdan-Lusztig polynomials in S_n

2002/06/17 by Gregory S. Warrington, Warrington, Gregory S.
Mathematics · #05E15 #20F55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E15 #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/0206164

9 pages, 4 figures

arxiv created 2002/06/17 · openalex publication_date 2002/06/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let w₀ denote the permutation [n,n-1,...,2,1]. We give two new explicit formulae for the Kazhdan-Lusztig polynomials P_w0w,w0x in S_n when x is a maximal element in the singular locus of the Schubert variety X_w. To do this, we utilize a standard identity that relates P_x,w and P_w0w,w0x.

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