On relations between the classical and the Kazhdan-Lusztig representations of symmetric groups and associated Hecke algebras.

DOI10.1016/j.jpaa.2005.03.015zbMath1090.20006OpenAlexW2074530597MaRDI QIDQ2573486

T. P. McDonough, C. A. Pallikaros

Publication date: 22 November 2005

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2005.03.015

zbMATH Keywords

Hecke algebrasKazhdan-Lusztig basesSpecht modulessymmetric groupsCoxeter systemscell modulescellular algebrasKazhdan-Lusztig representations

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Hecke algebras and their representations (20C08) Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (12)

James' conjecture for Hecke algebras of exceptional type. I. ⋮ Relations between the Clausen and Kazhdan-Lusztig representations of the symmetric group. ⋮ On double cosets with the trivial intersection property and Kazhdan-Lusztig cells in $S_n$ ⋮ Minimal determining sets for certain $W$-graph ideals ⋮ On embedding certain Kazhdan-Lusztig cells of \(S_n\) into cells of \(S_{n+1}\) ⋮ W-graph ideals. II. ⋮ RSK bases and Kazhdan-Lusztig cells ⋮ Bitableaux and zero sets of dual canonical basis elements ⋮ The ABC of \(p\)-cells ⋮ On ordered k-paths and rims for certain families of Kazhdan–Lusztig cells of Sn ⋮ On subsequences and certain elements which determine various cells in \(S_n\) ⋮ Specht modules and Kazhdan-Lusztig cells in type \(B_n\).

Uses Software

• GAP
• CHEVIE

Cites Work

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• On some geometric aspects of Bruhat orderings. II: The parabolic analogue of Kazhdan-Lusztig polynomials
• Relations between Young's natural and the Kazhdan-Lusztig representations of \(S_ n\)
• Representations of Coxeter groups and Hecke algebras
• Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function
• The representation theory of the symmetric groups
• Representations of affine Hecke algebras
• Some generic representations, \(W\)-graphs, and duality
• CHEVIE -- A system for computing and processing generic character tables
• Characters of Reductive Groups over a Finite Field. (AM-107)
• Representations of Hecke Algebras of General Linear Groups

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