An Explicit Formula for Szegő Kernels on the Heisenberg Group

Abstract

In this paper, we give an explicit formula for the Szegő kernel for (0, q) forms on the Heisenberg group Hn+1.

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Acknowledgements

The authors would like to thank the Institute for Mathematics, National University of Singapore for hospitality, a comfortable accommodation and financial support during their visits in May, 2017 for the program “Complex Geometry, Dynamical Systems and Foliation Theory”. A main part of this work was done when the first and third author were visiting the Institute of Mathematics, Academia Sinica in January, 2017. The authors thank the referees for carefully reading the manuscript and giving useful advices which improve the presentation of this paper.

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Correspondence to Hendrik Herrmann.

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In Memory of Professor Qikeng Lu (1927–2015)

The first author was partially supported by the CRC TRR 191: “Symplectic Structures in Geometry, Algebra and Dynamics”; the second author was partially supported by Taiwan Ministry of Science of Technology project (Grant No. 104-2628-M-001-003-MY2) and the Golden-Jade fellowship of Kenda Foundation; the third author was supported by National Natural Science Foundation of China (Grant No. 11501422)

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Herrmann, H., Hsiao, C.Y. & Li, X.S. An Explicit Formula for Szegő Kernels on the Heisenberg Group. Acta. Math. Sin.-English Ser. 34, 1225–1247 (2018). https://doi.org/10.1007/s10114-018-7324-2

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Keywords

  • Heisenberg group
  • Szegő kernels
  • complex Fourier integral operators

MR(2010) Subject Classification

  • 32V20
  • 32A25
  • 32W10