The Penrose Transform and the Exactness of the Tangential $$\pmb {k}$$-Cauchy–Fueter Complex on the Heisenberg Group

Abstract

The k-Cauchy–Fueter complex in quaternionic analysis was generalized to the Heisenberg group in a previous paper (Ren et al., in Adv Appl Clifford Algebras 30(2): Paper No. 20, 2020). But it is not known whether this differential complex is exact or not. In this paper, we apply the Penrose transform (the twistor method) to a double fibration of homogeneous spaces of $$\mathrm{SO}(2N,{\mathbb {C}})$$ to prove its exactness on the Heisenberg group.