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PreprintarXiv licencearXiv

Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space

  • Chunlin Liu
  • Giovanni Moreno
  • Haipan Shi
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Abstract

We study the equivalence classes of slice-regular functions f:Ω→ℍ on a symmetric slice domain Ω, and of their subclass made of polynomial slice-regular functions, with respect to the natural action of PGL(2,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 GL(2,ℍ).

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Cite

BibTeXRIS
BibTeX
@misc{liu2026classifying,
  title = {{Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space}},
  author = {Chunlin Liu and Giovanni Moreno and Haipan Shi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.22788},
  eprint = {2605.22788},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.22788},
}
RIS
TY  - UNPB
TI  - Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space
AU  - Chunlin Liu
AU  - Giovanni Moreno
AU  - Haipan Shi
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2605.22788
UR  - https://arxiv.org/abs/2605.22788
AB  - We study the equivalence classes of slice-regular functions f:Ω→ℍ on a symmetric slice domain Ω, and of their subclass made of polynomial slice-regular functions, with respect to the natural action of PGL(2,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 GL(2,ℍ).
ER  -