On homogeneous operators in the Cowen-Douglas class over polydisc

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.