Conjectures P1-P15 for Coxeter groups with complete graph

2019/02/28 by Xun Xie, Xie, Xun
Mathematics · #20C08 #20F55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1903.00078

openalex publication_date 2019/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using deceasing induction on 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.

Citations

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

Related

• Conjectures P1-P15 for hyperbolic Coxeter groups of rank 3
• Lusztig's a-function for Coxeter groups with complete graphs
• Classification of Coxeter groups with finitely many elements of a-value 2
• Generalized Jones traces and Kazhdan--Lusztig bases
• Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D