Skip to main content
SpringerLink
Log in

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso (D (0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(V N , F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(V N , F)) and Iso (D(V N , F))(0), where G (0) is the unit connected component of the Lie group G.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Piatetski-Shapiro I I. Geometry of Classical Domains and Theory of Automorphic Functions, Fizmatgiz, Moscow, 1961 (English transl). New York: Gordon and Breach, 1969

    Google Scholar 

  2. Vinberg E B, Gindikin S G, Piatetski-Shapiro I I. Classification and canonical realization of complex bounded homogeneous domains. Trudy Moskov Mat Obsc, 1963, 12: 359–388

    MATH  MathSciNet  Google Scholar 

  3. Xu Y C. On the automorphism group of the homogeneous bounded domains. Acta Math Sinica, Chinese Series, 1976, 19: 169–191

    MATH  Google Scholar 

  4. Xu Y C. On the isomorphism of homogeneous bounded domains. Acta Math Sinica, Chinese Series, 1977, 20: 248–266

    MATH  Google Scholar 

  5. Xu Y C. Theory of Complex Homogeneous Bounded Domains. Beijing-Dordrecht: Science Press & Kluwer Publishers, 2005

    MATH  Google Scholar 

  6. Hua L K. Harmonic analysis of functions of several complex variables in the classical domains. In: Transl Math Mono, Vol. 6. Providence: Amer Math Soc, 1963

    Google Scholar 

  7. Dorfmeister J. Homogeneous Siegel domains. Nagoya Math J, 1982, 86: 39–83

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Xu Yichao

  2. College of Mathematics and Information Sciences, Henan University, Kaifeng, 475001, China

    Chen Minru & Ma Songya

Authors
  1. Xu Yichao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Minru
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ma Songya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xu Yichao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, Y., Chen, M. & Ma, S. Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains. SCI CHINA SER A 49, 1392–1404 (2006). https://doi.org/10.1007/s11425-006-2009-1

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-006-2009-1

Keywords

Search

Navigation