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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 121, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.121 (Mi sigma1420) 		 
Matrix Bailey Lemma and the Star-Triangle Relation

Kamil Yu. Magadova, Vyacheslav P. Spiridonovbc

a Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Laboratory of Theoretical Physics, Dubna, Moscow Region, 141980 Russia
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DOI: https://doi.org/10.3842/SIGMA.2018.121
Abstract: We compare previously found finite-dimensional matrix and integral operator realizations of the Bailey lemma employing univariate elliptic hypergeometric functions. With the help of residue calculus we explicitly show how the integral Bailey lemma can be reduced to its matrix version. As a consequence, we demonstrate that the matrix Bailey lemma can be interpreted as a star-triangle relation, or as a Coxeter relation for a permutation group.
Keywords: elliptic hypergeometric functions; Bailey lemma; star-triangle relation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
This work is partially supported by Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. no. 14.641.31.0001.
Received: August 10, 2018; in final form October 30, 2018; Published online November 10, 2018
Bibliographic databases:
Document Type: Article
MSC: 33D60; 33E20
Language: English
Citation: Kamil Yu. Magadov, Vyacheslav P. Spiridonov, “Matrix Bailey Lemma and the Star-Triangle Relation”, SIGMA, 14 (2018), 121, 13 pp.
Citation in format AMSBIB
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