Towards a combinatorial classification of skew Schur functions

DOI10.1090/S0002-9947-09-04683-2zbMath1228.05293arXivmath/0608446OpenAlexW2075313214MaRDI QIDQ5322899

Peter R. W. McNamara, Stephanie Van Willigenburg

Publication date: 23 July 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608446

zbMATH Keywords

symmetric functionWeyl moduleskew Schur functionribbonJacobi-Trudi determinantHamel-Goulden determinant

Mathematics Subject Classification ID

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

Related Items (17)

Equality of multiplicity free skew characters ⋮ A Hopf algebraic approach to Schur function identities ⋮ Gelfand-Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions ⋮ Equality of \(P\)-partition generating functions. ⋮ Inequality of a class of near-ribbon skew Schur \(Q\)-functions ⋮ Skew quasisymmetric Schur functions and noncommutative Schur functions ⋮ Maximal supports and Schur-positivity among connected skew shapes ⋮ On principal hook length partitions and Durfee sizes in skew characters ⋮ Classifying the near-equality of ribbon Schur functions ⋮ Coincidences among skew Schur functions ⋮ Necessary conditions for Schur-maximality ⋮ \(P\)-partition generating function equivalence of naturally labeled posets ⋮ \(P\)-partition generating function equivalence of naturally labeled posets ⋮ The CDE property for skew vexillary permutations ⋮ Positivity results on ribbon Schur function differences ⋮ Support equalities among ribbon Schur functions ⋮ Minuscule Doppelgängers, The Coincidental down-Degree Expectations Property, and Rowmotion

Cites Work

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• Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions
• On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients
• Matrix Analysis
• The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
• Vanishing and nonvanishing criteria in Schubert calculus
• A generalization of the Littlewood-Richardson rule

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