Conjectures P1-P15 for Coxeter groups with complete graph
arXiv:1903.00078
Abstract
We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using deceasing induction on -values and a kind of decomposition formula of Kazhdan-Lusztig basis elements. As a byproduct, we give a description of the left, right, and two-sided cells. In the appendix, we prove P1-P15 for right-angled Coxeter groups by the same methods.
48 pages, in version 2, we add a new section \S9