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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 017, 32 pages      arXiv:2406.18337      https://doi.org/10.3842/SIGMA.2025.017

The Geometry of Generalised Spinr Spinors on Projective Spaces

Diego Artacho a and Jordan Hofmann b
a) Imperial College London, London SW7 2AZ, UK
b) King's College London, London WC2R 2LS, UK

Received July 01, 2024, in final form March 01, 2025; Published online March 11, 2025

Abstract
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 OP2 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 r for which this space is non-zero. Additionally, we demonstrate some geometric implications of the existence of special spinr spinors on these spaces.

Key words: special spinors; projective spaces; generalized spin structures; spinc; spinh.

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