Asymptotic Formulas for Macdonald Polynomials and the boundary of the $(q, t)$-Gelfand-Tsetlin graph

Cesar Cuenca

Published 2017-04-08Version 1

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-Panova in arXiv:1301.0634 [math.PR], and are expected to provide tools for the study of statistical mechanical models, representation theory and random matrices. As first application of our formulas, we characterize the boundary of the $(q, t)-$deformation of the Gelfand-Tsetlin graph.