A₂ Macdonald polynomials: a separation of variables

1995/12/04 by Vladimir V. Mangazeev, Mangazeev, V. V.
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9512003

openalex publication_date 1995/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct a discrete linear operator K which transforms A₂ Macdonald polynomials into the product of two basic 3ϕ₂ hypergeometric series with known arguments. The action of the operator K on power sums in two variables can be reduced to a generalization of one particular case of the Bailey's summation formula for a very-well-poised 6ψ₆ series. We also propose the conjecture for a transformation of 6ψ₆ series with different arguments.

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