Conjectures P1-P15 for Coxeter groups with complete graph

Xie, Xun

doi:10.1016/j.aim.2021.107565

Cited by 2 publications

(2 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Cells of some other specific Coxeter systems (especially those with small ranks or complete Coxeter diagrams) have also been computed, often on a case-by-case basis via carefully designed algorithms. For example, the paper [36] treats cells in the Coxeter group F 4 , [33] treats C4 , [1] treats H 3 and H 4 , [9] and [14] treat E 8 ; the paper [20] studies affine Weyl groups of rank 2, and the papers [37,38] deal with Coxeter systems with complete Coxeter diagrams. For a more comprehensive summary of the cell literature, see [7, §26].…”

Section: Introductionmentioning

confidence: 99%

Kazhdan–Lusztig cells of a-value 2 in a(2)-finite Coxeter systems

Green¹,

Xu²

2023

Algebraic Combinatorics

View full text Add to dashboard Cite

A Coxeter group is said to be a(2)-finite if it has finitely many elements of a-value (in the sense of Lusztig) equal to 2. In this paper, we give explicit combinatorial descriptions of the left, right, and two-sided Kazhdan-Lusztig cells of a-value 2 in an irreducible a(2)-finite Coxeter group. In particular, we introduce elements we call stubs to parameterize the onesided cells and we characterize the one-sided cells via both star operations and weak Bruhat orders. We also compute the cardinalities of all the one-sided and two-sided cells of a-value 2 in irreducible a(2)-finite Coxeter groups.

show abstract

Section: Introductionmentioning

confidence: 99%

Kazhdan–Lusztig cells of a-value 2 in a(2)-finite Coxeter systems

Green¹,

Xu²

2023

Algebraic Combinatorics

View full text Add to dashboard Cite

show abstract

“…Cells of some other specific Coxeter systems (especially those with small ranks or complete Coxeter diagrams) have also been computed, often on a case-by-case basis via carefully designed algorithms. For example, the paper [40] treats cells in the Coxeter group F 4 , [36] treats C4 , [1] treats H 3 and H 4 , [10] and [16] treat E 8 ; the paper [23] studies affine Weyl groups of rank 2, and the papers [41,42] deal with Coxeter systems with complete Coxeter diagrams. For a more comprehensive summary of the cell literature, see [8, §26].…”

Section: Introductionmentioning

confidence: 99%

Kazhdan--Lusztig cells of $\mathbf{a}$-value 2 in $\mathbf{a}(2)$-finite Coxeter systems

Green¹,

Xu²

2021

Preprint

View full text Add to dashboard Cite

A Coxeter group is said to be a(2)-finite if it has finitely many elements of a-value 2 in the sense of Lusztig. In this paper, we give explicit combinatorial descriptions of the left, right, and two-sided Kazhdan-Lusztig cells of a-value 2 in an irreducible a(2)-finite Coxeter group. In particular, we introduce elements we call stubs to parameterize the one-sided cells and we characterize the one-sided cells via both star operations and weak Bruhat orders. We also compute the cardinalities of all the one-sided and two-sided cells.

show abstract

Conjectures P1-P15 for Coxeter groups with complete graph

Cited by 2 publications

References 30 publications

Kazhdan–Lusztig cells of a-value 2 in a(2)-finite Coxeter systems

Kazhdan–Lusztig cells of a-value 2 in a(2)-finite Coxeter systems

Kazhdan--Lusztig cells of $\mathbf{a}$-value 2 in $\mathbf{a}(2)$-finite Coxeter systems

Contact Info

Product

Resources

About