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An Elliptic Hypergeometric Function Approach to Branching Rules

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. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.3842/sigma.2020.142DOIArticle
https://arxiv.org/abs/2007.03174arXivDiscussion Paper
ORCID:
AuthorORCID
Warnaar, S. Ole0000-0002-9786-0175
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.
Funders:
Funding AgencyGrant Number
Australian Research CouncilDP170102648
Korea Institute for Advanced StudyMG067302
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
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:22 Jan 2021 22:26

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