Scholarlink

<p>In the first part, we describe the recent work (Upmeier in Atti Accad Naz Lincei Cl Sci Fis Mat Nat 32:565–591, 2021; Upmeier in J Reine Angew Math (Crelle J) 799:155–187, 2023; Upmeier in Complex Anal Oper Theory 17:74, 2023) of the author concerning the eigenbundle of analytic Hilbert modules over bounded symmetric domains of arbitrary rank. In the second part, we develop in full detail the realization of the fibers of the eigenbundle in terms of Kähler geometry, as holomorphic section modules over certain flag manifolds. Here a new feature is to work directly on the complex strata (Kepler manifolds) instead of just the so-called tripotents. This makes the complex analytic properties more transparent.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Hilbert modules and Kähler geometry

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年9月20日

查看全文
  • Harald Upmeier

摘要

In the first part, we describe the recent work (Upmeier in Atti Accad Naz Lincei Cl Sci Fis Mat Nat 32:565–591, 2021; Upmeier in J Reine Angew Math (Crelle J) 799:155–187, 2023; Upmeier in Complex Anal Oper Theory 17:74, 2023) of the author concerning the eigenbundle of analytic Hilbert modules over bounded symmetric domains of arbitrary rank. In the second part, we develop in full detail the realization of the fibers of the eigenbundle in terms of Kähler geometry, as holomorphic section modules over certain flag manifolds. Here a new feature is to work directly on the complex strata (Kepler manifolds) instead of just the so-called tripotents. This makes the complex analytic properties more transparent.