The Geometry of Generalised Spin$^r$ Spinors on Projective Spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912268939165696 |
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| author | Artacho, Diego Hofmann, Jordan |
| author_facet | Artacho, Diego Hofmann, Jordan |
| contents | In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spin$^r$ context. We find new invariant spin$^r$ spinors on the projective spaces $\mathbb{CP}^n$, $\mathbb{HP}^n$, and the Cayley plane $\mathbb{OP}^2$ for all their homogeneous realisations. Specifically, for each of these realisations, we provide a complete description of the space of invariant spin$^r$ 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 spin$^r$ spinors on these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Geometry of Generalised Spin$^r$ Spinors on Projective Spaces Artacho, Diego Hofmann, Jordan Differential Geometry Representation Theory 53C27, 15A66, 57R15 In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spin$^r$ context. We find new invariant spin$^r$ spinors on the projective spaces $\mathbb{CP}^n$, $\mathbb{HP}^n$, and the Cayley plane $\mathbb{OP}^2$ for all their homogeneous realisations. Specifically, for each of these realisations, we provide a complete description of the space of invariant spin$^r$ 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 spin$^r$ spinors on these spaces. |
| title | The Geometry of Generalised Spin$^r$ Spinors on Projective Spaces |
| topic | Differential Geometry Representation Theory 53C27, 15A66, 57R15 |
| url | https://arxiv.org/abs/2406.18337 |