Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 142, 52 pages      arXiv:2007.03174      https://doi.org/10.3842/SIGMA.2020.142
Contribution to the Special Issue on Elliptic Integrable Systems, Special Functions and Quantum Field Theory

An Elliptic Hypergeometric Function Approach to Branching Rules

Chul-hee Lee a, Eric M. Rains b and S. Ole Warnaar c
a) School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Korea
b) Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
c) School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia

Received July 08, 2020, in final form December 09, 2020; Published online December 23, 2020

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.

Key words: branching formulas; elliptic hypergeometric series; elliptic Selberg integrals; interpolation functions; Koornwinder polynomials; Littlewood identities; Macdonald polynomials.

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