Noncrossing partitions, fully commutative elements and bases of the Temperley–Lieb algebra

DOI10.1142/S0218216516500358zbMath1365.57016arXiv1409.6500OpenAlexW2963891224MaRDI QIDQ2809231

Thomas Gobet

Publication date: 27 May 2016

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.6500

zbMATH Keywords

fully commutative elementsArtin braid groupdual braid monoidTemperley-Lieb algebra: noncrossing partitions

Mathematics Subject Classification ID

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

Related Items (6)

A Heyting algebra on Dyck paths of type \(A\) and \(B\) ⋮ Dual garside structures and Coxeter sortable elements ⋮ On some Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation ⋮ Noncrossing partitions and Bruhat order ⋮ Dual braid monoids, Mikado braids and positivity in Hecke algebras ⋮ Coxeter-Catalan combinatorics and Temperley-Lieb algebras

Uses Software

• GAP

Cites Work

• Unnamed Item
• Noncrossing partitions and Bruhat order
• An improved tableau criterion for Bruhat order
• On the fully commutative elements of Coxeter groups
• Foundations of Garside theory
• The dual braid monoid
• Commuting Families in Hecke and Temperley-Lieb Algebras
• DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS
• A TEMPERLEY-LIEB BASIS COMING FROM THE BRAID GROUP
• Catalan Numbers
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• A partial order on the symmetric group and new \(K(\pi,1)\)'s for the braid groups

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