Breakthroughs in the theory of Macdonald polynomials

DOI10.1073/pnas.0409705102zbMath1208.05148OpenAlexW2052547752WikidataQ29391326 ScholiaQ29391326MaRDI QIDQ5293353

Adriano M. Garsia, Jeffery B. Remmel

Publication date: 30 June 2007

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.0409705102

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Hypergeometric functions associated with root systems (33C67)

Related Items (7)

Bijection between oriented maps and weighted non-oriented maps ⋮ Higher order Macdonald operators with stability properties and their applications ⋮ A combinatorial formula for Macdonald polynomials ⋮ Cumulants of Jack symmetric functions and the $b$-conjecture ⋮ Dual immaculate quasisymmetric functions expand positively into Young quasisymmetric Schur functions ⋮ A probabilistic interpretation of the Macdonald polynomials ⋮ Strong factorization property of Macdonald polynomials and higher-order Macdonald's positivity conjecture

Cites Work

• On certain graded \(S_ n\)-modules and the \(q\)-Kostka polynomials
• Lattice diagram polynomials and extended Pieri rules
• Plethystic formulas for Macdonald \(q,t\)-Kostka coefficients
• Rodrigues formulas for the Macdonald polynomials
• Tableau atoms and a new Macdonald positivity conjecture
• Affine Hecke algebras and raising operators for Macdonald polynomials
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• Longest Increasing and Decreasing Subsequences
• A Proof of Some q-Analogues of Selberg’s Integral for $k=1$
• A graded representation model for Macdonald's polynomials.
• Combinatorial theory of Macdonald polynomials I: Proof of Haglund's formula
• A combinatorial model for the Macdonald polynomials
• On the Representations of the Symmetric Group

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