A New Generalisation of Macdonald Polynomials
Alexandr Garbali, Jan de Gier, Michael Wheeler
Communications in Mathematical Physics | Springer | Published : 2017
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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Awarded by National Science Foundation
We gratefully acknowledge support from the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), and MW acknowledges support by an Australian Research Council DECRA. We would like to thank V. V. Mangazeev and Z. Tsuboi for pointing out the references  and  respectively. JdG would like to thank the KITP Program New approaches to non-equilibrium and random systems: KPZ integrability, universality, applications and experiments, supported in part by the National Science Foundation under Grant No. NSF PHY11-25915, and with MW the program Statistical mechanics and combinatorics at the Simons Center for Geometry and Physics, Stony Brook University, where part of this work were completed. MW would like to thank Alexei Borodin for kind hospitality at MIT and very stimulating discussions on related themes.