Matrix Bailey Lemma and the Star-Triangle Relation
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 conseque...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209883 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Matrix Bailey Lemma and the Star-Triangle Relation / K.Yu. Magadov, V.P. Spiridonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862610222810398720 |
|---|---|
| author | Magadov, K.Yu. Spiridonov, V.P. |
| author_facet | Magadov, K.Yu. Spiridonov, V.P. |
| citation_txt | Matrix Bailey Lemma and the Star-Triangle Relation / K.Yu. Magadov, V.P. Spiridonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T12:55:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209883 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T12:55:39Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Magadov, K.Yu. Spiridonov, V.P. 2025-11-28T09:42:06Z 2018 Matrix Bailey Lemma and the Star-Triangle Relation / K.Yu. Magadov, V.P. Spiridonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D60; 33E20 arXiv: 1810.10806 https://nasplib.isofts.kiev.ua/handle/123456789/209883 https://doi.org/10.3842/SIGMA.2018.121 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. This work is partially supported by the Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. no. 14.641.31.0001. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Matrix Bailey Lemma and the Star-Triangle Relation Article published earlier |
| spellingShingle | Matrix Bailey Lemma and the Star-Triangle Relation Magadov, K.Yu. Spiridonov, V.P. |
| title | Matrix Bailey Lemma and the Star-Triangle Relation |
| title_full | Matrix Bailey Lemma and the Star-Triangle Relation |
| title_fullStr | Matrix Bailey Lemma and the Star-Triangle Relation |
| title_full_unstemmed | Matrix Bailey Lemma and the Star-Triangle Relation |
| title_short | Matrix Bailey Lemma and the Star-Triangle Relation |
| title_sort | matrix bailey lemma and the star-triangle relation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209883 |
| work_keys_str_mv | AT magadovkyu matrixbaileylemmaandthestartrianglerelation AT spiridonovvp matrixbaileylemmaandthestartrianglerelation |