Non-trivial Kazhdan-Lusztig coefficients of affine Weyl groups

Abstract

In this paper we show that the leading coefficient $\hat{I}¼(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in an affine Weyl group of type ${\tilde{B}}_n$ (resp. ${\tilde{C}}_n$ or ${\tilde{D}}_n$) is $n$ (resp. $n+1$).

30 pages