Asymptotic lowest two-sided cell

Abstract

To a Coxeter system $(W,S)$ (with $S$ finite) and a weight function $L : W \to \NM$ is associated a partition of $W$ into Kazhdan-Lusztig (left, right or two-sided) $L$-cells. Let $S^{\circ }=\{s\in S|L(s)=0\}$, $S^{+}=\{s\in S|L(s)>0\}$ and let $C$ be a Kazhdan-Lusztig (left, right or two-sided) $L$-cell. According to the semicontinuity conjecture of the first author, there should exist a positive natural number $m$ such that, for any weight function $L' : W \to \NM$ such that $L(s^{+})=L^{\prime }(s^{+})>m{L}^{\prime }(s^{\circ })$ for all $s^{+}\in S^{+}$ and $s^{\circ }\in S^{\circ }$, $C$ is a union of Kazhdan-Lusztig (left, right or two-sided) $L^{\prime }$-cells. The aim of this paper is to prove this conjecture whenever $(W,S)$ is an affine Weyl group and $C$ is contained in the lowest two-sided $L$-cell.

45 pages, 10 figures

References in corpus (1)

• Some computations about Kazhdan-Lusztig cells in affine Weyl groups of rank 2