Harald Upmeier
Published 2022-05-25Version 1
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 K\"ahler 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.
K-invariant Hilbert Modules and Singular Vector Bundles on Bounded Symmetric Domains
Weighted composition operators on weighted Bergman spaces of bounded symmetric domains
Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains
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