The Geometry of Generalised Spinʳ Spinors on Projective Spaces

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Artacho, Diego, Hofmann, Jordan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212874
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Geometry of Generalised Spinʳ Spinors on Projective Spaces. Diego Artacho and Jordan Hofmann. SIGMA 21 (2025), 017, 32 pages

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...