Dual garside structures and Coxeter sortable elements

DOI10.4171/JCA/42MaRDI QIDQ2194417

Thomas Gobet

Publication date: 26 August 2020

Published in: Journal of Combinatorial Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.05418

zbMATH Keywords

Coxeter groupsArtin groupsnoncrossing partitions

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Uses Software

• CHEVIE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A categorification of non-crossing partitions
• A Garside presentation for Artin-Tits groups of type \(\widetilde C_n\).
• Dual braid monoids, Mikado braids and positivity in Hecke algebras
• On the Hurwitz action in finite Coxeter groups
• Noncrossing partitions and the shard intersection order
• Climbing elements in finite Coxeter groups.
• On positivity in Hecke algebras
• Noncrossing partitions and Bruhat order
• Reflection subgroups of Coxeter systems
• A new approach to the word and conjugacy problems in the braid groups
• Some properties of crossings and partitions
• On cycle decompositions in Coxeter groups
• Artin monoids inject in their groups
• Rigidity of Coxeter groups and Artin groups
• Springer theory in braid groups and the Birman-Ko-Lee monoid.
• CHEVIE -- A system for computing and processing generic character tables
• The development version of the \texttt{CHEVIE} package of \texttt{GAP3}.
• Foundations of Garside theory
• Finite complex reflection arrangements are \(K(\pi,1)\)
• Twisted filtrations of Soergel bimodules and linear Rouquier complexes
• The 2-braid group and Garside normal form
• Dual presentations of braid groups of affine type \(\widetilde A\).
• On minimal lengths of expressions of Coxeter group elements as products of reflections
• Noncrossing partitions, fully commutative elements and bases of the Temperley–Lieb algebra
• A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements
• Combinatorics of Coxeter Groups
• Sortable elements in infinite Coxeter groups
• The dual braid monoid
• Clusters, Coxeter-sortable elements and noncrossing partitions
• Three-Dimensional Realizations of Braids
• Simple dual braids, noncrossing partitions and Mikado braids of type Dn
• Noncrossing Partitions for the GroupDn
• A PARTIAL ORDER ON THE ORTHOGONAL GROUP
• Non-crossing partition lattices in finite real reflection groups