A Laurent Phenomenon for the Cayley Plane
We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated with the cominuscule representation of ₆. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the ₙ Dynkin diagrams for ≤ 6. We conjecture...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212162 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Laurent Phenomenon for the Cayley Plane. Oliver Daisey and Tom Ducat. SIGMA 20 (2024), 033, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862746378854203392 |
|---|---|
| author | Daisey, Oliver Ducat, Tom |
| author_facet | Daisey, Oliver Ducat, Tom |
| citation_txt | A Laurent Phenomenon for the Cayley Plane. Oliver Daisey and Tom Ducat. SIGMA 20 (2024), 033, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated with the cominuscule representation of ₆. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the ₙ Dynkin diagrams for ≤ 6. We conjecture the existence of a further finite type LPA associated to the Freudenthal variety of type ₇.
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| first_indexed | 2026-03-21T18:10:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212162 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:10:59Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Daisey, Oliver Ducat, Tom 2026-01-30T08:15:46Z 2024 A Laurent Phenomenon for the Cayley Plane. Oliver Daisey and Tom Ducat. SIGMA 20 (2024), 033, 18 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 14M17 arXiv:2310.10223 https://nasplib.isofts.kiev.ua/handle/123456789/212162 https://doi.org/10.3842/SIGMA.2024.033 We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated with the cominuscule representation of ₆. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the ₙ Dynkin diagrams for ≤ 6. We conjecture the existence of a further finite type LPA associated to the Freudenthal variety of type ₇. Both authors would like to thank Anna Felikson for some very useful discussions whilst undertaking this research project. We are also grateful to the anonymous referees for their detailed feedback. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Laurent Phenomenon for the Cayley Plane Article published earlier |
| spellingShingle | A Laurent Phenomenon for the Cayley Plane Daisey, Oliver Ducat, Tom |
| title | A Laurent Phenomenon for the Cayley Plane |
| title_full | A Laurent Phenomenon for the Cayley Plane |
| title_fullStr | A Laurent Phenomenon for the Cayley Plane |
| title_full_unstemmed | A Laurent Phenomenon for the Cayley Plane |
| title_short | A Laurent Phenomenon for the Cayley Plane |
| title_sort | laurent phenomenon for the cayley plane |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212162 |
| work_keys_str_mv | AT daiseyoliver alaurentphenomenonforthecayleyplane AT ducattom alaurentphenomenonforthecayleyplane AT daiseyoliver laurentphenomenonforthecayleyplane AT ducattom laurentphenomenonforthecayleyplane |