This article is cited in 9 papers

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

Cesar Cuenca

Department of Mathematics, Massachusetts Institute of Technology, USA

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 first application of our formulas, we characterize the boundary of the $(q,t)$-deformation of the Gelfand–Tsetlin graph when $t = q^{\theta}$ and $\theta$ is a positive integer.

Keywords: Branching graph; Macdonald polynomials; Gelfand–Tsetlin graph.

MSC: 33D52; 33D90; 60B15; 60C05

Received: April 21, 2017; in final form December 9, 2017; Published online January 2, 2018

Language: English

DOI: 10.3842/SIGMA.2018.001

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