The right-type groups are nilpotent Lie groups of step two having a pair of anticommutative operators, and many aspects of quaternionic analysis can be generalized to this kind of groups. In this paper, we use the twistor transformation to study the tangential k-Cauchy–Fueter equations and quaternionic k-regular functions on these groups. We introduce the twistor space over the \((4n+r)\)-dimensional complex right-type groups and use twistor transformation to construct an explicit Radon–Penrose type integral formula to solve the holomorphic tangential k-Cauchy–Fueter equation on these groups. When restricted to the real right-type group, this formula provides solutions to tangential k-Cauchy–Fueter equations. In particular, it gives us many k-regular polynomials.

右类型群是第二步的幂等 Lie 群，具有一对反交换运算符，四元数分析的许多方面都可以推广到这种群。在本文中，我们使用扭曲变换来研究这些群的切向 k-Cauchy-Fueter 方程和四元数 k-正则函数。我们在 \（（4n+r）\） 维复数右类型群上引入扭曲空间，并使用扭曲变换构造一个显式的 Radon-Penrose 型积分公式，以求解这些群上的全态切向 k-Cauchy-Fueter 方程。当仅限于实右类型组时，此公式提供切向 k-Cauchy-Fueter 方程的解。特别是，它为我们提供了许多 k 正则多项式。