The Lipschitz Spinor-Higher Horosphere Correspondence
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918475381866496 |
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| author | Zymaris, Orion |
| author_facet | Zymaris, Orion |
| contents | In a paper of Mathews, an isomorphism is constructed between two-component complex spinors and horospheres in H^3 carrying `spin decorations'. A recent arXiv preprint of Mathews and Varsha arXiv:2412.06572 extends this result to the case of `quaternionic spinors' and spin decorated horospheres in H^4.
The following work generalises these results to an equivariant correspondence between two-component `Lipschitz spinors' with entries drawn from the Lipschitz group of a Clifford algebra, null multiflags in generalised Minkowski space, and higher-dimensional horospheres that carry an extension of the Mathews spin decoration. This correspondence allows spinors to be applied to horospheres in any dimension of hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Lipschitz Spinor-Higher Horosphere Correspondence Zymaris, Orion Geometric Topology 15A66 In a paper of Mathews, an isomorphism is constructed between two-component complex spinors and horospheres in H^3 carrying `spin decorations'. A recent arXiv preprint of Mathews and Varsha arXiv:2412.06572 extends this result to the case of `quaternionic spinors' and spin decorated horospheres in H^4. The following work generalises these results to an equivariant correspondence between two-component `Lipschitz spinors' with entries drawn from the Lipschitz group of a Clifford algebra, null multiflags in generalised Minkowski space, and higher-dimensional horospheres that carry an extension of the Mathews spin decoration. This correspondence allows spinors to be applied to horospheres in any dimension of hyperbolic space. |
| title | The Lipschitz Spinor-Higher Horosphere Correspondence |
| topic | Geometric Topology 15A66 |
| url | https://arxiv.org/abs/2604.27397 |