Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph
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 provid...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209463 |
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| Cite this: | Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph / C. Cuenca // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 48 назв. — англ. |
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Cuenca, C. 2025-11-21T19:15:48Z 2018 Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph / C. Cuenca // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 48 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D52; 33D90; 60B15; 60C05 arXiv: 1704.02429 https://nasplib.isofts.kiev.ua/handle/123456789/209463 https://doi.org/10.3842/SIGMA.2018.001 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. It is my pleasure to thank Alexei Borodin for his generous sharing of time and ideas. I am equally indebted to Vadim Gorin for his interest in my work, for many helpful discussions, and for sharing some of his notes on the q-GT graph. This work would not exist without them. I would also like to thank Jiaoyang Huang for being an excellent sounding board at the beginning stage of this project, Konstantin Matveev for his expert help with the software Mathematica, and Grigori Olshanski for comments in a previous draft of this paper and for asking a question that led to my proof of Theorem 1.3. The suggestions of the referees helped improve this text greatly; many thanks are due to them. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph |
| spellingShingle |
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph Cuenca, C. |
| title_short |
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph |
| title_full |
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph |
| title_fullStr |
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph |
| title_full_unstemmed |
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph |
| title_sort |
asymptotic formulas for macdonald polynomials and the boundary of the (q,t)-gelfand-tsetlin graph |
| author |
Cuenca, C. |
| author_facet |
Cuenca, C. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209463 |
| citation_txt |
Asymptotic Formulas for Macdonald Polynomials and the Boundary of the (q,t)-Gelfand-Tsetlin Graph / C. Cuenca // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 48 назв. — англ. |
| work_keys_str_mv |
AT cuencac asymptoticformulasformacdonaldpolynomialsandtheboundaryoftheqtgelfandtsetlingraph |
| first_indexed |
2025-12-07T16:57:56Z |
| last_indexed |
2025-12-07T16:57:56Z |
| _version_ |
1850886074562248704 |