Stratified Hilbert Modules on Bounded Symmetric Domains

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