THE REPRESENTATIVE DOMAIN OF A HOMOGENEOUS BOUNDED DOMAIN

• ISHI Hideyuki

  Graduate School of Mathematics Nagoya University

• KAI Chifune

  Faculty of Mathematics and Physics Institute of Science and Engineering Kanazawa University

Abstract

The representative domain gives a nice realization for a homogeneous bounded domain, which is a generalization of the Harish-Chandra realization for a symmetric bounded domain. We show that the representative domain coincides with the image of the Cayley transform introduced by Penney and Nomura. As an application, we see that a homogeneous bounded domain is symmetric if and only if its representative domain is convex.

Journal

• Kyushu Journal of Mathematics

  Kyushu Journal of Mathematics 64 (1), 35-47, 2009

  Faculty of Mathematics, Kyushu University

Keywords

• Bergman kernel
• representative domain
• minimal domain
• homogeneous bounded domain
• symmetric bounded domain
• Cayley transform

Details

• CRID: 1390001205228726656
• NII Article ID: 130000259012
• NII Book ID: AA10994346
• DOI: 10.2206/kyushujm.64.35
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/64/1/64_1_35/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed