Communications in Mathematical Physics

, Volume 352, Issue 2, pp 773–804 | Cite as

A New Generalisation of Macdonald Polynomials

  • Alexandr Garbali
  • Jan de Gier
  • Michael WheelerEmail author


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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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia

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