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Stratified Hilbert Modules on Bounded Symmetric Domains

In: Multivariable Operator Theory

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  • Harald Upmeier

    (Universität Marburg, Fachbereich Mathematik)

Abstract

We analyze the “eigenbundle” (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank r, giving rise to complex-analytic fibre spaces which are stratified of length $$r+1.$$ r + 1 . The fibres are described in terms of Kähler geometry as line bundle sections over flag manifolds, and the metric embedding is determined by taking derivatives of reproducing kernel functions. Important examples are the determinantal ideals defined by vanishing conditions along the various strata of the stratification.

Suggested Citation

  • Harald Upmeier, 2023. "Stratified Hilbert Modules on Bounded Symmetric Domains," Springer Books, in: Ernst Albrecht & Raúl Curto & Michael Hartz & Mihai Putinar (ed.), Multivariable Operator Theory, pages 799-831, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-50535-5_29
    DOI: 10.1007/978-3-031-50535-5_29
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