Leading coefficients of Kazhdan-Lusztig polynomials and fully commutative elements

Abstract

Let W be a Coxeter group of type Ãn-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). © 2008 Springer Science+Business Media, LLC.