The Geometry of Generalised Spinʳ Spinors on Projective Spaces
In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spinʳ context. We find new invariant spinʳ spinors on the projective spaces ℂℙⁿ, ℍℙⁿ, and the Cayley plane ℙ² for all their homogeneous realisations. Specifically, for each of these realisat...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212874 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Geometry of Generalised Spinʳ Spinors on Projective Spaces. Diego Artacho and Jordan Hofmann. SIGMA 21 (2025), 017, 32 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862743673663389696 |
|---|---|
| author | Artacho, Diego Hofmann, Jordan |
| author_facet | Artacho, Diego Hofmann, Jordan |
| citation_txt | The Geometry of Generalised Spinʳ Spinors on Projective Spaces. Diego Artacho and Jordan Hofmann. SIGMA 21 (2025), 017, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spinʳ context. We find new invariant spinʳ spinors on the projective spaces ℂℙⁿ, ℍℙⁿ, and the Cayley plane ℙ² for all their homogeneous realisations. Specifically, for each of these realisations, we provide a complete description of the space of invariant spinʳ spinors for the minimum value of for which this space is non-zero. Additionally, we demonstrate some geometric implications of the existence of special spinʳ spinors on these spaces.
|
| first_indexed | 2026-03-21T18:30:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212874 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:30:54Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Artacho, Diego Hofmann, Jordan 2026-02-13T13:49:09Z 2025 The Geometry of Generalised Spinʳ Spinors on Projective Spaces. Diego Artacho and Jordan Hofmann. SIGMA 21 (2025), 017, 32 pages 1815-0659 2020 Mathematics Subject Classification: 53C27; 15A66; 57R15 arXiv:2406.18337 https://nasplib.isofts.kiev.ua/handle/123456789/212874 https://doi.org/10.3842/SIGMA.2025.017 In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spinʳ context. We find new invariant spinʳ spinors on the projective spaces ℂℙⁿ, ℍℙⁿ, and the Cayley plane ℙ² for all their homogeneous realisations. Specifically, for each of these realisations, we provide a complete description of the space of invariant spinʳ spinors for the minimum value of for which this space is non-zero. Additionally, we demonstrate some geometric implications of the existence of special spinʳ spinors on these spaces. The authors are grateful to Travis Schedler for his contributions to the representation-theoretical aspect of the paper, and to Marie-Am´elie Lawn for her comments and fruitful discussions. We are grateful to the referees for their helpful comments. D. Artacho is funded by the UK Engineering and Physical Sciences Research Council (EPSRC), grant EP/W5238721. J. Hofmann was supported by the Engineering and Physical Sciences Research Council [EP/L015234/1, EP/W522429/1]; the EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory: University College London, King’s College London, and Imperial College London); and a DAAD Short Term Research Grant for a research stay at Philipps-Universität Marburg. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Geometry of Generalised Spinʳ Spinors on Projective Spaces Article published earlier |
| spellingShingle | The Geometry of Generalised Spinʳ Spinors on Projective Spaces Artacho, Diego Hofmann, Jordan |
| title | The Geometry of Generalised Spinʳ Spinors on Projective Spaces |
| title_full | The Geometry of Generalised Spinʳ Spinors on Projective Spaces |
| title_fullStr | The Geometry of Generalised Spinʳ Spinors on Projective Spaces |
| title_full_unstemmed | The Geometry of Generalised Spinʳ Spinors on Projective Spaces |
| title_short | The Geometry of Generalised Spinʳ Spinors on Projective Spaces |
| title_sort | geometry of generalised spinʳ spinors on projective spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212874 |
| work_keys_str_mv | AT artachodiego thegeometryofgeneralisedspinrspinorsonprojectivespaces AT hofmannjordan thegeometryofgeneralisedspinrspinorsonprojectivespaces AT artachodiego geometryofgeneralisedspinrspinorsonprojectivespaces AT hofmannjordan geometryofgeneralisedspinrspinorsonprojectivespaces |