Bilateral Bailey Lattices and Andrews-Gordon Type Identities
We show that the Bailey lattice can be extended to a bilateral version in just a few lines from the bilateral Bailey lemma, using a very simple lemma transforming bilateral Bailey pairs relative to into bilateral Bailey pairs relative to /. Using this and similar lemmas, we give bilateral versions...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/213182 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Bilateral Bailey Lattices and Andrews-Gordon Type Identities. Jehanne Dousse, Frédéric Jouhet and Isaac Konan. SIGMA 21 (2025), 032, 32 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727342254718976 |
|---|---|
| author | Dousse, Jehanne Jouhet, Frédéric Konan, Isaac |
| author_facet | Dousse, Jehanne Jouhet, Frédéric Konan, Isaac |
| citation_txt | Bilateral Bailey Lattices and Andrews-Gordon Type Identities. Jehanne Dousse, Frédéric Jouhet and Isaac Konan. SIGMA 21 (2025), 032, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that the Bailey lattice can be extended to a bilateral version in just a few lines from the bilateral Bailey lemma, using a very simple lemma transforming bilateral Bailey pairs relative to into bilateral Bailey pairs relative to /. Using this and similar lemmas, we give bilateral versions and simple proofs of other (new and known) Bailey lattices, including a Bailey lattice of Warnaar and the inverses of Bailey lattices of Lovejoy. As consequences of our bilateral point of view, we derive new -versions of the Andrews-Gordon identities, Bressoud's identities, a new companion to Bressoud's identities, and the Bressoud-Göllnitz-Gordon identities. Finally, we give a new elementary proof of another very general identity of Bressoud using one of our Bailey lattices.
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| first_indexed | 2026-03-21T10:37:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213182 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T10:37:46Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dousse, Jehanne Jouhet, Frédéric Konan, Isaac 2026-02-16T16:34:44Z 2025 Bilateral Bailey Lattices and Andrews-Gordon Type Identities. Jehanne Dousse, Frédéric Jouhet and Isaac Konan. SIGMA 21 (2025), 032, 32 pages 1815-0659 2020 Mathematics Subject Classification: 11P84; 05A30; 33D15; 33D90 arXiv:2307.02346 https://nasplib.isofts.kiev.ua/handle/123456789/213182 https://doi.org/10.3842/SIGMA.2025.032 We show that the Bailey lattice can be extended to a bilateral version in just a few lines from the bilateral Bailey lemma, using a very simple lemma transforming bilateral Bailey pairs relative to into bilateral Bailey pairs relative to /. Using this and similar lemmas, we give bilateral versions and simple proofs of other (new and known) Bailey lattices, including a Bailey lattice of Warnaar and the inverses of Bailey lattices of Lovejoy. As consequences of our bilateral point of view, we derive new -versions of the Andrews-Gordon identities, Bressoud's identities, a new companion to Bressoud's identities, and the Bressoud-Göllnitz-Gordon identities. Finally, we give a new elementary proof of another very general identity of Bressoud using one of our Bailey lattices. The authors are grateful to Jeremy Lovejoy for very helpful comments on an earlier version of this paper. The authors also thank the anonymous referees for their very careful reading of the paper and for their great suggestions for improvement and future research directions. The authors are partially funded by the ANR COMBIN´e ANR-19-CE48-0011. JD is funded by the SNSF Eccellenza grant number PCEFP2 202784. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bilateral Bailey Lattices and Andrews-Gordon Type Identities Article published earlier |
| spellingShingle | Bilateral Bailey Lattices and Andrews-Gordon Type Identities Dousse, Jehanne Jouhet, Frédéric Konan, Isaac |
| title | Bilateral Bailey Lattices and Andrews-Gordon Type Identities |
| title_full | Bilateral Bailey Lattices and Andrews-Gordon Type Identities |
| title_fullStr | Bilateral Bailey Lattices and Andrews-Gordon Type Identities |
| title_full_unstemmed | Bilateral Bailey Lattices and Andrews-Gordon Type Identities |
| title_short | Bilateral Bailey Lattices and Andrews-Gordon Type Identities |
| title_sort | bilateral bailey lattices and andrews-gordon type identities |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213182 |
| work_keys_str_mv | AT doussejehanne bilateralbaileylatticesandandrewsgordontypeidentities AT jouhetfrederic bilateralbaileylatticesandandrewsgordontypeidentities AT konanisaac bilateralbaileylatticesandandrewsgordontypeidentities |