Monomials and Temperley-Lieb algebras

DOI10.1006/jabr.1996.6930zbMath0899.20018OpenAlexW2045452781MaRDI QIDQ1355614

Richard M. Green, C. Kenneth Fan

Publication date: 8 July 1997

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

Full work available at URL: https://doi.org/10.1006/jabr.1996.6930

zbMATH Keywords

Hecke algebrasKazhdan-Lusztig basesTemperley-Lieb algebrasWeyl groupsgeneratorsmonomial basessimply laced Coxeter groups

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (15)

Combinatorial properties of the Temperley-Lieb algebra of a Coxeter group. ⋮ Kazhdan-Lusztig immanants and products of matrix minors ⋮ Cell structures on the blob algebra ⋮ A diagrammatic Temperley-Lieb categorification ⋮ Categorification of the Temperley-Lieb algebra by bimodules. ⋮ Algebraic methods for chromatic polynomials. ⋮ Structure of a Hecke algebra quotient ⋮ Dual braid monoids, Mikado braids and positivity in Hecke algebras ⋮ A skein action of the symmetric group on noncrossing partitions ⋮ The Kazhdan-Lusztig basis and the Temperley-Lieb quotient in type \(D\) ⋮ Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations ⋮ Fully commutative Kazhdan-Lusztig cells ⋮ \(A_{2}\)-web immanants ⋮ Framization of a Temperley-Lieb algebra of type \(\mathtt{B}\) ⋮ On planar algebras arising from hypergroups.

Cites Work

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• The Kazhdan-Lusztig cells in certain affine Weyl groups
• Hecke algebra representations of braid groups and link polynomials
• Two-sided cells in the affine Weyl group of type \(\tilde A_{n-1}\)
• Representations of Coxeter groups and Hecke algebras
• On the fully commutative elements of Coxeter groups
• The representation theory of the Temperley-Lieb algebras
• \(q\)-Schur algebras, asymptotic forms, and quantum \(SL_ n\)
• Cellular algebras
• A Hecke algebra quotient and some combinatorial applications
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem

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