Lee, Chul-hee and Rains, Eric M. and Warnaar, S. Ole (2020) An Elliptic Hypergeometric Function Approach to Branching Rules. Symmetry, Integrability and Geometry, Methods and Applications (SIGMA), 16 . Art. No. 142. ISSN 1815-0659. doi:10.3842/sigma.2020.142. https://resolver.caltech.edu/CaltechAUTHORS:20210122-141416267
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Abstract
We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose some conjectural branching rules and allied conjectures exhibiting a novel type of vanishing behaviour involving partitions with empty 2-cores.
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| Additional Information: | © 2020 National Academy of Sciences of Ukraine. This paper is a contribution to the Special Issue on Elliptic Integrable Systems, Special Functions and Quantum Field Theory. The full collection is available at https://www.emis.de/journals/SIGMA/elliptic-integrablesystems.html. We thank one of the referees of our paper for suggesting we compare the branching rule (1.12a) with [15, Conjectures 9.12 and 9.13] by Hoshino and Shiraishi. This work was supported by the Australian Research Council Discovery Grant DP170102648 and a KIAS Individual Grant (MG067302) at Korea Institute for Advanced Study. | |||||||||
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| Subject Keywords: | branching formulas; elliptic hypergeometric series; elliptic Selberg integrals; interpolation functions; Koornwinder polynomials; Littlewood identities; Macdonald polynomials | |||||||||
| Classification Code: | 2020 Mathematics Subject Classification: 05E05; 05E10; 20C33; 33D05; 33D52; 33D67 | |||||||||
| DOI: | 10.3842/sigma.2020.142 | |||||||||
| Record Number: | CaltechAUTHORS:20210122-141416267 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210122-141416267 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 107664 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 22 Jan 2021 22:26 | |||||||||
| Last Modified: | 16 Nov 2021 19:05 |
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