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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. doi:10.3842/sigma.2020.142.

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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
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URLURL TypeDescription Paper
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 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.
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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107664
Deposited By: Tony Diaz
Deposited On:22 Jan 2021 22:26
Last Modified:16 Nov 2021 19:05

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