Determinantal expressions for Macdonald polynomials

1998/08/11 by Luc Lapointe, L. Lapointe, Lapointe, L. +6
Mathematics · Physics and Astronomy · #05E05 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.CO #math.QA #msc:05E05

paper · pdf · doi:10.48550/arxiv.math/9808050

21 pages, TeX, to be published in IMRN

arxiv created 1998/08/11 · openalex publication_date 1998/08/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the action of classical operators associated to the Macdonald polynomials on the basis of Schur functions, S_λ[X(t-1)/(q-1)], can be reduced to addition in λ-rings. This provides explicit formulas for the Macdonald polynomials expanded in this basis as well as in the ordinary Schur basis, S_λ[X], and the monomial basis, m_λ[X].

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