Conjectures P1-P15 for Coxeter groups with complete graph

Xun Xie

doi:10.1016/j.aim.2021.107565

Conjectures P1-P15 for Coxeter groups with complete graph

Xun Xie

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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Abstract

We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using decreasing induction on a-values and a kind of factorization 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.

Original language	English
Article number	107565
Journal	Advances in Mathematics
Volume	379
DOIs	https://doi.org/10.1016/j.aim.2021.107565
Publication status	Published - 5 Mar 2021

Keywords

Conjectures P1-P15
Coxeter groups with complete graph
Factorization formula
Lusztig's a-function
Right-angled Coxeter groups

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10.1016/j.aim.2021.107565

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Xie, X. (2021). Conjectures P1-P15 for Coxeter groups with complete graph. Advances in Mathematics, 379, Article 107565. https://doi.org/10.1016/j.aim.2021.107565

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abstract = "We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using decreasing induction on a-values and a kind of factorization 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.",

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AB - We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using decreasing induction on a-values and a kind of factorization 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.

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Conjectures P1-P15 for Coxeter groups with complete graph

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Keywords

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