Structure of a Hecke algebra quotient

DOI10.1090/S0894-0347-97-00222-1zbMath0861.20042MaRDI QIDQ5690902

C. Kenneth Fan

Publication date: 9 January 1997

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Temperley-Lieb algebrasCoxeter groupsirreducible representationsIwahori-Hecke algebrassemisimple algebrasCoxeter graphscell theory

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Representations of quivers and partially ordered sets (16G20)

Related Items

Kazhdan-Lusztig immanants and products of matrix minors, Diagram calculus for a type affine \(C\) Temperley-Lieb algebra. II., Semi-simplicity of Temperley-Lieb algebras of type D, The enumeration of fully commutative elements of Coxeter groups, Parabolic Temperley-Lieb modules and polynomials, Gröbner–Shirshov bases for Temperley–Lieb algebras of types B and D, Kazhdan-Lusztig cells of \(\mathbf{a} \)-value 2 in \(\mathbf{a}(2)\)-finite Coxeter systems, Fibonacci determinants with Cameron's operator, The Birman-Murakami-Wenzl algebras of type \(\mathbf E_n\)., Morphisms from Hecke algebras to graphic Temperley-Lieb algebras, Fully commutative elements in finite and affine Coxeter groups, Eriksson's numbers game and finite Coxeter groups, The Birman–Murakami–Wenzl Algebras of Type D_n, The Kazhdan-Lusztig basis and the Temperley-Lieb quotient in type \(D\), Unnamed Item, Generalized Jones traces and Kazhdan-Lusztig bases., Characterization of cyclically fully commutative elements in finite and affine Coxeter groups, ON THE MARKOV TRACE FOR TEMPERLEY–LIEB ALGEBRAS OF TYPE E_n, Comparison of \(a\)-functions, Cameron's operator in terms of determinants and hypergeometric numbers, Acyclic heaps of pieces. I., The Dieck-Temperley-Lieb algebras of type B and C in Brauer algebras, Smoothness of Schubert varieties via patterns in root subsystems, Tabular algebras and their asymptotic versions., On 321-avoiding permutations in affine Weyl groups

Cites Work

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• On the fully commutative elements of Coxeter groups
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• A polynomial invariant for knots via von Neumann algebras
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem