Commuting Families in Hecke and Temperley-Lieb Algebras

DOI10.1017/S0027763000009740zbMath1217.20002arXiv0710.0596MaRDI QIDQ3182448

Manuela Mazzocco, Arun Ram, Thomas Halverson

Publication date: 8 October 2009

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.0596

zbMATH Keywords

Hecke algebrasTemperley-Lieb algebraseigenvaluesquantum groupsJucys-Murphy elementsCasimir elementsBrauer diagrams

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Representation theory for linear algebraic groups (20G05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Representation theory of associative rings and algebras (16G99) Associative rings and algebras arising under various constructions (16S99)

Related Items (14)

On the computation of fusion over the affine Temperley-Lieb algebra ⋮ Quantum spin chains from Onsager algebras and reflection \(K\)-matrices ⋮ Topological defects in lattice models and affine Temperley-Lieb algebra ⋮ Quantum walled Brauer algebra: commuting families, Baxterization, and representations ⋮ A physical approach to the classification of indecomposable Virasoro representations from the blob algebra ⋮ A cellular basis for the generalized Temperley-Lieb algebra and Mahler measure ⋮ Centralizing the centralizers ⋮ On Neeman’s gradient flows ⋮ Set-partition tableaux and representations of diagram algebras ⋮ Dual braid monoids, Mikado braids and positivity in Hecke algebras ⋮ On cellular algebras with Jucys Murphy elements. ⋮ Noncrossing partitions, fully commutative elements and bases of the Temperley–Lieb algebra ⋮ Affine braid group, JM elements and knot homology ⋮ The local conserved quantities of the closed XXZ chain

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