Leading coefficients of Kazhdan--Lusztig polynomials and fully commutative elements

2008/01/10 by R.M. Green, Green, R. M.
Mathematics · #20C08 #20F55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.0801.1650

openalex publication_date 2008/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W be a Coxeter group of type \widetildeA_n-1. We show that the leading coefficient, μ(x, w), of the Kazhdan--Lusztig polynomial P_{x, w} is always equal to 0 or 1 if x is fully commutative (and w is arbitrary).

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