Stratified Hilbert Modules on Bounded Symmetric Domains

Harald Upmeier ()
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Harald Upmeier: Universität Marburg, Fachbereich Mathematik

A chapter in Multivariable Operator Theory, 2023, pp 799-831 from Springer

Abstract: 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.

Keywords: Bounded symmetric domain; Hilbert module; Complex-analytic fibre space; Flag manifold; Jordan triple; Primary 32M15; 46E22; Secondary 14M12; 17C36; 47B35 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-50535-5_29

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DOI: 10.1007/978-3-031-50535-5_29

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