On homogeneous operators in the Cowen-Douglas class over polydisc

Prahllad Deb

Research output: Contribution to journalArticlepeer-review

Abstract

We classify all tuples of operators in the Cowen-Douglas class of rank 1 and 2 homogeneous with respect to Möbn using Wilkins’ classification of homogeneous hermitian holomorphic vector bundles over bounded symmetric domains. It is also observed that these homogeneous tuples can be re-alised as the adjoint of the tuples of multiplication operators on the quotient Hilbert modules obtained from certain submodules of the weighted Bergman modules on the open unit polydisc.

Original languageEnglish
Pages (from-to)402-419
Number of pages18
JournalNew York Journal of Mathematics
Volume28
StatePublished - 1 Jan 2022

Keywords

  • Bounded symmetric domain
  • Cowen-Douglas class
  • Curvature
  • Hermitian holomorphic homogeneous vector bundles
  • Hilbert modules
  • Homogeneous operators

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