Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space
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arXiv
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| Format: | Preprint |
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2026
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| author | Liu, Chunlin Moreno, Giovanni Shi, Haipan |
| author_facet | Liu, Chunlin Moreno, Giovanni Shi, Haipan |
| contents | We study the equivalence classes of slice-regular functions $f:Ω\to\mathbb{H}$ on a symmetric slice domain $Ω$, and of their subclass made of polynomial slice-regular functions, with respect to the natural action of $\mathrm{PGL}(2,\mathbb{H})$ and its subgroups, by employing the twistor construction. In particular, we characterize slice--regular functions whose twistor lift is planar and belongs to a given orbit, and we find normal classes of slice-regular polynomials with respect to the action of a parabolic subgroup of $\mathrm{GL}(2,\mathbb{H})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22788 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space Liu, Chunlin Moreno, Giovanni Shi, Haipan Differential Geometry 6W22, 30G35, 53C28 We study the equivalence classes of slice-regular functions $f:Ω\to\mathbb{H}$ on a symmetric slice domain $Ω$, and of their subclass made of polynomial slice-regular functions, with respect to the natural action of $\mathrm{PGL}(2,\mathbb{H})$ and its subgroups, by employing the twistor construction. In particular, we characterize slice--regular functions whose twistor lift is planar and belongs to a given orbit, and we find normal classes of slice-regular polynomials with respect to the action of a parabolic subgroup of $\mathrm{GL}(2,\mathbb{H})$. |
| title | Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space |
| topic | Differential Geometry 6W22, 30G35, 53C28 |
| url | https://arxiv.org/abs/2605.22788 |