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 \(r+1.\) 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.
Dedicated to the Memory of Jörg Eschmeier.
Communicated by Mihai Putinar.
This article is part of the topical collection “Multivariable Operator Theory. The Jörg Eschmeier Memorial” edited by Raul Curto, Michael Hartz, Mihai Putinar and Ernst Albrecht.
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Upmeier, H. (2023). Stratified Hilbert Modules on Bounded Symmetric Domains. In: Albrecht, E., Curto, R., Hartz, M., Putinar, M. (eds) Multivariable Operator Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-50535-5_29
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DOI: https://doi.org/10.1007/978-3-031-50535-5_29
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-50534-8
Online ISBN: 978-3-031-50535-5
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