We show that the "eigenbundle" (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank r is a "singular" vector bundle (linearly fibrered complex analytic space) which decomposes as a stratified sum of homogeneous vector bundles along a canonical stratification of length r+1. The fibres are realized in terms of representation theory on the normal space of the strata.
Stratified Hilbert Modules on Bounded Symmetric Domains
Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains
Weighted composition operators on weighted Bergman spaces of bounded symmetric domains
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