Conjectures P1-P15 for Coxeter groups with complete graph

Abstract

We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using deceasing induction on $\mathbf{a}$-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.

arXiv comment48 pages, in version 2, we add a new section \S9

References in corpus (6)

• Lusztig's $a$-function for Coxeter groups with complete graphs
• A factorization theorem for affine Kazhdan-Lusztig basis elements
• Conjectures on tilting modules and antispherical $p$-cells
• A decomposition formula for the Kazhdan-Lusztig basis of affine Hecke algebras of rank 2
• The boundness of weighted Coxeter groups of rank 3
• The lowest two-sided cell of weighted Coxeter groups of rank 3

Cited by in corpus (1)

• Conjectures P1-P15 for hyperbolic Coxeter groups of rank 3