Vanishing ideals of lattice diagram determinants

DOI10.1006/jcta.2002.3268zbMath1009.05137arXivmath/0107155OpenAlexW1969686332MaRDI QIDQ696909

Nantel Bergeron, Jean-Christophe Aval

Publication date: 12 September 2002

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0107155

zbMATH Keywords

harmonic polynomialsvanishing idealslattice diagramsymmetric modules

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)

Related Items (4)

Bitableau bases for Garsia-Haiman modules of hollow type ⋮ Spaces of lattice diagram polynomials in one set of variables ⋮ Schur partial derivative operators ⋮ Resolutions of De Concini–Procesi Ideals of Hooks

Cites Work

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• Spaces of lattice diagram polynomials in one set of variables
• Defining ideals of the closures of the conjugacy classes and representations of the Weyl groups
• Symmetric functions, conjugacy classes and the flag variety
• On certain graded \(S_ n\)-modules and the \(q\)-Kostka polynomials
• Lattice diagram polynomials and extended Pieri rules
• A simple proof of the Littlewood-Richardson rule and applications.
• Monomial bases related to the \(n!\) conjecture
• On certain spaces of lattice diagram determinants
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• A graded representation model for Macdonald's polynomials.

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