The Geometry of Generalised Spinʳ Spinors on Projective Spaces

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2025
• Hauptverfasser: Artacho, Diego, Hofmann, Jordan
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2025
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/212874
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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...