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.

中文翻译：

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彭罗斯变换和切线的精确度$$ \ pmb {k} $$ k-海森堡群上的库奇-费特复合体

四元离子分析中的k -Cauchy-Fueter络合物在先前的论文中被推广到Heisenberg组（Ren等人，在Adv Appl Clifford Algebras 30（2）：论文第20号，2020年）。但是尚不清楚该微分复数是否精确。在本文中，我们将Penrose变换（扭曲方法）应用于\（\ mathrm {SO}（2N，{\ mathbb {C}}）\）的齐次空间的双纤化，以证明其在Heisenberg群上的正确性。