The Racah Algebra of Rank 2: Properties, Symmetries and Representation
The goals of this paper are threefold. First, we provide a new ''universal'' definition for the Racah algebra of rank 2 as an extension of the rank-1 Racah algebra where the generators are indexed by subsets, and any three disjoint indexing sets define a subalgebra isomorphic to...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212610 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Racah Algebra of Rank 2: Properties, Symmetries and Representation. Sarah Post and Sébastien Bertrand. SIGMA 20 (2024), 085, 21 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862545483466014720 |
|---|---|
| author | Post, Sarah Bertrand, Sébastien |
| author_facet | Post, Sarah Bertrand, Sébastien |
| citation_txt | The Racah Algebra of Rank 2: Properties, Symmetries and Representation. Sarah Post and Sébastien Bertrand. SIGMA 20 (2024), 085, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The goals of this paper are threefold. First, we provide a new ''universal'' definition for the Racah algebra of rank 2 as an extension of the rank-1 Racah algebra where the generators are indexed by subsets, and any three disjoint indexing sets define a subalgebra isomorphic to the rank-1 case. With this definition, we explore some of the properties of the algebra, including verifying that these natural assumptions are equivalent to other defining relations in the literature. Second, we look at the symmetries of the generators of the rank-2 Racah algebra. Those symmetries allow us to partially make an abstraction of the choice of the generators and write relations and properties in a different format. Last, we provide a novel representation of the Racah algebra. This new representation requires only one generator to be diagonal and is based on an expansion of the split basis representation from the rank-1 Racah algebra.
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| first_indexed | 2026-03-21T11:36:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212610 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:36:28Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Post, Sarah Bertrand, Sébastien 2026-02-09T08:06:04Z 2024 The Racah Algebra of Rank 2: Properties, Symmetries and Representation. Sarah Post and Sébastien Bertrand. SIGMA 20 (2024), 085, 21 pages 1815-0659 2020 Mathematics Subject Classification: 81R12; 20C35 arXiv:2402.08944 https://nasplib.isofts.kiev.ua/handle/123456789/212610 https://doi.org/10.3842/SIGMA.2024.085 The goals of this paper are threefold. First, we provide a new ''universal'' definition for the Racah algebra of rank 2 as an extension of the rank-1 Racah algebra where the generators are indexed by subsets, and any three disjoint indexing sets define a subalgebra isomorphic to the rank-1 case. With this definition, we explore some of the properties of the algebra, including verifying that these natural assumptions are equivalent to other defining relations in the literature. Second, we look at the symmetries of the generators of the rank-2 Racah algebra. Those symmetries allow us to partially make an abstraction of the choice of the generators and write relations and properties in a different format. Last, we provide a novel representation of the Racah algebra. This new representation requires only one generator to be diagonal and is based on an expansion of the split basis representation from the rank-1 Racah algebra. The authors would like to thank Nicolas Crampé and Eric Ragoucy for the fruitful discussion on the subject. The authors would also like to thank the anonymous referees for their comments and suggestions. SP would like to acknowledge the Simons Foundation Collaboration grant #3192112, as well as support as a CRM-Simons professorship, and the hospitality of the CRM for a fruitful visit, while much of the research was conducted. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Racah Algebra of Rank 2: Properties, Symmetries and Representation Article published earlier |
| spellingShingle | The Racah Algebra of Rank 2: Properties, Symmetries and Representation Post, Sarah Bertrand, Sébastien |
| title | The Racah Algebra of Rank 2: Properties, Symmetries and Representation |
| title_full | The Racah Algebra of Rank 2: Properties, Symmetries and Representation |
| title_fullStr | The Racah Algebra of Rank 2: Properties, Symmetries and Representation |
| title_full_unstemmed | The Racah Algebra of Rank 2: Properties, Symmetries and Representation |
| title_short | The Racah Algebra of Rank 2: Properties, Symmetries and Representation |
| title_sort | racah algebra of rank 2: properties, symmetries and representation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212610 |
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