A new generalisation of Macdonald polynomials

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.

26 pages, LaTeX

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Cited by in corpus (3)

• An Ising-type formulation of the six-vertex model
• Observables of coloured stochastic vertex models and their polymer limits
• Transition probability and total crossing events in the multi-species asymmetric exclusion process