Leading coefficients of Kazhdan–Lusztig polynomials and fully commutative elements

Let W be a Coxeter group of type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\widetilde{A}_{n-1}$\end{document} . We show that the leading coefficient, μ(x,w), of the Kazhdan–Lusztig polynomial Px,w is always equal to 0 or 1 if x is fully commutative (and w is arbitrary).