1993/04/15 by Adriano M. Garsia, Mark Haiman · 160 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Conjecture #Difference polynomials #Macdonald polynomials #Mathematics #Orthogonal polynomials #Pure mathematics #Representation (politics)
paper · doi:10.1073/pnas.90.8.3607
published in Proceedings of the National Academy of Sciences 90(8), 3607-3610 (National Academy of Sciences)
openalex publication_date 1993/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
We define doubly graded Sn modules Rmu for which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Klambdamu. Assuming one fundamental conjecture, the modules Rmu can be given several equivalent definitions, which we discuss. We prove the conjectures in various special cases.