Multiple left regular representations generated by alternants

DOI10.1006/jcta.2000.3089zbMath0963.05135OpenAlexW2012291069MaRDI QIDQ1584649

François Bergeron, Adriano M. Garsia, Glenn Tesler

Publication date: 21 June 2001

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

Full work available at URL: https://doi.org/10.1006/jcta.2000.3089

zbMATH Keywords

representations of symmetric groupsMacdonald polynomialscomplex reflection groupsFrobenius characteristiclattice diagram polynomials

Mathematics Subject Classification ID

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

Related Items (9)

Recent progress in algebraic combinatorics ⋮ Catalan paths and quasi-symmetric functions ⋮ Hilbert functions of \(\mathfrak{S}_n\)-stable artinian Gorenstein algebras ⋮ Symmetric complete intersections ⋮ \(r\)-Qsym is free over Sym ⋮ Bitableau bases for Garsia-Haiman modules of hollow type ⋮ Spaces of lattice diagram polynomials in one set of variables ⋮ Inverse systems and regular representations ⋮ Schur partial derivative operators

Cites Work

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• On the eigenvalues of representations of reflection groups and wreath products
• Lattice diagram polynomials and extended Pieri rules
• Isotypic decompositions of lattice determinants
• Some graded representations of the complex reflection groups
• Plethystic formulas for Macdonald \(q,t\)-Kostka coefficients
• A graded representation model for Macdonald's polynomials.
• Differential Equations Invariant Under Finite Reflection Groups
• Finite Unitary Reflection Groups
• A new class of symmetric functions

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