Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph

Abstract

We introduce Macdonald characters and use algebraic properties of Macdonald polynomials to study them. As a result, we produce several formulas for Macdonald characters, which are generalizations of those obtained by Gorin and Panova in [Ann. Probab. 43 (2015), 3052-3132], and are expected to provide tools for the study of statistical mechanical models, representation theory, and random matrices. As the first application of our formulas, we characterize the boundary of the (q,t)-deformation of the Gelfand-Tsetlin graph when t=qθ and θ is a positive integer.