New York Journal of Mathematics
Volume 28 (2022), 402-419


Prahllad Deb

On homogeneous operators in the Cowen-Douglas class over polydisc

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Published: February 4, 2022.
Keywords: Hilbert modules, Cowen-Douglas class, Homogeneous operators, Hermitian holomorphic homogeneous vector bundles, Curvature, Bounded symmetric domain.
Subject: Primary: 47B32, 47B13, Secondary: 53C07.

We classify all tuples of operators in the Cowen-Douglas class of rank 1 and 2 homogeneous with Mobn using Wilkins' classification of homogeneous hermitian holomorphic vector bundles over bounded symmetric domains. It is also observed that these homogeneous tuples can be realised 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.


The research of the author was supported by the Ph.D. Fellowship at Indian Institute of Science Education and Research Kolkata (IISER Kolkata) and the Post-doctoral fellowship in the Department of Mathematics at Ben-Gurion University in the Negev (BGU). Although most of the results in this paper are from the Ph.D. thesis of the author submitted to IISER Kolkata, the research was completed during the Post-doctoral training in the Department of Mathematics, Faculty of Natural Sciences at BGU.

Author information

Prahllad Deb:
Department of Mathematics
Ben-Gurion University in the Negev
Beer-Sheva, Israel - 84105