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

Symmetry Integrability and Geometry-Methods and Applications

article

Cesar Cuenca¹ 

[1] Department of Mathematics, Massachusetts Institute of Technology

关键词: Branching graph;    Macdonald polynomials;    Gelfand–Tsetlin graph;   

DOI  :  10.3842/SIGMA.2018.001

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown