The k-Cauchy–Fueter operator and the tangential k-Cauchy–Fueter operator are the quaternionic counterpart of Cauchy–Riemann operator and the tangential Cauchy–Riemann operator in the theory of several complex variables, respectively. In Wang (On the boundary complex of the k-Cauchy–Fueter complex, arXiv:2210.13656), Wang introduced the notion of right-type groups, which have the structure of nilpotent Lie groups of step-two, and many aspects of quaternionic analysis can be generalized to this kind of group. In this paper we generalize the right-type group to any step-two case, and introduce the generalization of Cauchy–Fueter operator on \({\mathbb {H}}^n\times {\mathbb {R}}^r.\) Then we establish the Bochner–Martinelli type formula for tangential k-Cauchy–Fueter operator on stratified right-type groups.

k - Cauchy -Fueter算子和切向k -Cauchy-Fueter算子分别是多复变量理论中Cauchy-Riemann算子和切向Cauchy-Riemann算子的四元数对应物。在 Wang（On the boundary complex of the k -Cauchy-Fueter complex, arXiv:2210.13656）中，Wang 介绍了右型群的概念，它具有二阶幂零李群的结构，以及四元数分析的许多方面可以推广到这种群体。在本文中，我们将右类型群推广到任何二步情况，并引入 Cauchy–Fueter 算子在\({\mathbb {H}}^n\times {\mathbb {R}}^r 上的推广。 \)然后我们建立了分层右型群上切线k -Cauchy-Fueter算子的Bochner-Martinelli型公式。