Fully commutative elements in the Weyl and affine Weyl groups.

DOI10.1016/j.jalgebra.2004.08.036zbMath1079.20059OpenAlexW2075953501MaRDI QIDQ1764827

Jian-yi Shi

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.08.036

zbMATH Keywords

affine Weyl groupsfully commutative elementsleft cellsdistinguished involutions\(a\)-functions

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Directed graphs (digraphs), tournaments (05C20)

Related Items (12)

Left cells containing a fully commutative element. ⋮ Leading coefficients of Kazhdan-Lusztig polynomials and fully commutative elements. ⋮ Diagram calculus for a type affine \(C\) Temperley-Lieb algebra. II. ⋮ Parabolic Temperley-Lieb modules and polynomials ⋮ A note on fully commutative elements in complex reflection groups ⋮ Kazhdan-Lusztig cells of \(\mathbf{a} \)-value 2 in \(\mathbf{a}(2)\)-finite Coxeter systems ⋮ Left Cells witha-Value 4 in the Affine Weyl Groups (i = 6, 7, 8) ⋮ Classification of Coxeter groups with finitely many elements of \(\mathfrak{a}\)-value 2 ⋮ Left-connectedness of some left cells in certain Coxeter groups of simply-laced type. ⋮ The Laurent polynomials \(M^s_{y,w}\) in the Hecke algebra with unequal parameters. ⋮ The enumeration of fully commutative affine permutations ⋮ Generalized Jones traces and Kazhdan-Lusztig bases.

Cites Work

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• Fully commutative elements and Kazhdan–Lusztig cells in the finite and affine Coxeter groups
• Fully commutative elements and Kazhdan-Lusztig cells in the finite and affine Coxeter groups, II
• Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations
• Fully commutative Kazhdan-Lusztig cells
• Conjugacy relation on Coxeter elements

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