A Conjecture about Raising Operators for Macdonald Polynomials

Abstract

A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Jozefiak's expression for the two-row Macdonald polynomials, and also with Lassalle and Schlosser's formula for partitions with length three.

13 pages

References in corpus (4)

• Inversion of the Pieri formula for Macdonald polynomials
• A Commutative Family of Integral Transformations and Basic Hypergeometric Series. I. Eigenfunctions
• An analytic formula for Macdonald polynomials
• A Commutative Family of Integral Transformations and Basic Hypergeometric Series. II. Eigenfunctions and Quasi-Eigenfunctions

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• A Commutative Family of Integral Transformations and Basic Hypergeometric Series. I. Eigenfunctions
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• Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
• Construction of eigenfunctions for the elliptic Ruijsenaars difference operators
• Basic Properties of Non-Stationary Ruijsenaars Functions
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• An Elliptic Hypergeometric Function Approach to Branching Rules
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Closed-form propagator of the Calogero model
• Branching Formula for $q$-Toda Function of Type B