Green polynomials at roots of unity and Springer modules for the symmetric groups

DOI10.1016/j.aim.2006.10.008zbMath1116.05089OpenAlexW2074391194MaRDI QIDQ881965

Hideaki Morita

Publication date: 23 May 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2006.10.008

zbMATH Keywords

symmetric functionsroots of unitypermutation enumeration

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10)

Related Items (5)

Garsia-Haiman modules for hook partitions and Green polynomials with two variables ⋮ Factorization formulas for Macdonald polynomials ⋮ Tabloids and weighted sums of characters of certain modules of the symmetric groups ⋮ Hall-Littlewood polynomials and fixed point enumeration ⋮ A formula of Lascoux-Leclerc-Thibon and representations of symmetric groups

Cites Work

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• Decomposition of Green polynomials of type \(A\) and Springer modules for hooks and rectangles.
• A variant of the induction theorem for Springer representations.
• On the eigenvalues of representations of reflection groups and wreath products
• Symmetric functions, conjugacy classes and the flag variety
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• A construction of representations of Weyl groups
• A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups
• Green polynomials and Hall-Littlewood functions at roots of unity
• The coinvariant algebra of the symmetric group as a direct sum of induced modules.
• Regular elements of finite reflection groups
• A formula of Lascoux-Leclerc-Thibon and representations of symmetric groups
• The Characters of the Finite General Linear Groups
• Springer's regular elements over arbitrary fields
• Hall–Littlewood polynomials at roots of 1 and modular representations of the symmetric group
• Twisted Invariant Theory for Reflection Groups

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