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...
Збережено в:
| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| ISSN: | 1815-0659 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/213182 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Bilateral Bailey Lattices and Andrews-Gordon Type Identities. Jehanne Dousse, Frédéric Jouhet and Isaac Konan. SIGMA 21 (2025), 032, 32 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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| ISSN: | 1815-0659 |