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A New Generalisation of Macdonald Polynomials

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Abstract

We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters (q, t) and polynomial in a further two parameters (u, v). We evaluate these polynomials explicitly as a matrix product. At u = v = 0 they reduce to Macdonald polynomials, while at q = 0, u = v = s they recover a family of inhomogeneous symmetric functions originally introduced by Borodin.

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Authors and Affiliations

  1. ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia

    Alexandr Garbali, Jan de Gier & Michael Wheeler

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  1. Alexandr Garbali
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  2. Jan de Gier
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  3. Michael Wheeler
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Correspondence to Michael Wheeler.

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Communicated by A. Borodin

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Garbali, A., de Gier, J. & Wheeler, M. A New Generalisation of Macdonald Polynomials. Commun. Math. Phys. 352, 773–804 (2017). https://doi.org/10.1007/s00220-016-2818-1

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  • DOI: https://doi.org/10.1007/s00220-016-2818-1

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