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

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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.

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Acknowledgements

The authors would like to thank the referees for many valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, China

    Yun Shi

  2. Department of Mathematics, Linyi University, Linyi, 276005, China

    Qingyan Wu

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  1. Yun Shi
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  2. Qingyan Wu
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Correspondence to Qingyan Wu.

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This article is part of the Topical Collection on Proceedings ICCA 12, Hefei, 2020, edited by Guangbin Ren, Uwe Kähler, Rafał Abłamowicz, Fabrizio Colombo, Pierre Dechant, G. Stacey Staples, Wei Wang.

Y. Shi is partially supported by National Nature Science Foundation in China (Nos. 11801508, 11971425); Q. Wu is partially supported by National Nature Science Foundation in China (No. 12071197), the Natural Science Foundation of Shandong Province (Nos. ZR2019YQ04, 2020KJI002).

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Shi, Y., Wu, Q. The Penrose Transform and the Exactness of the Tangential \(\pmb {k}\)-Cauchy–Fueter Complex on the Heisenberg Group. Adv. Appl. Clifford Algebras 31, 33 (2021). https://doi.org/10.1007/s00006-021-01129-4

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  • DOI: https://doi.org/10.1007/s00006-021-01129-4

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