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, arXiv:1301.0634], 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.

References in corpus (3)

• Fluctuations of particle systems determined by Schur generating functions
• Jack polynomials and free cumulants
• Structure coefficients for Jack characters: approximate factorization property

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• Type classification of extremal quantized characters
• Asymptotic Behavior of Multiplicative Spherical Integrals and S-transform