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arXiv · 2605.22788

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 $f:\Omega\to\mathbb{H}$ on a symmetric slice domain $\Omega$, 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 $\mathrm{GL}(2,\mathbb{H})$.

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Chunlin Liu, Giovanni Moreno, Haipan Shi. 2026-05-21. Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space. https://arxiv.org/abs/2605.22788

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