Homogeneous Hermitian holomorphic vector bundles and operators in the Cowen-Douglas class over the poly-disc

In this article, we obtain two sets of results. The first set results are for the case bi-disc while second describe in part, which these carry over to general poly-disc. A classification irreducible hermitian holomorphic vector bundles D2, homogeneous with respect Möb×Möb, is obtained assuming that associated representations multiplicity-free. Among ones give rise an operator Cowen-Douglas class D2 rank 1,2 or 3 determined. Any bundle 2 Dn, n-fold direct product group Möb shown be a tensor n D. them, n−1 line and one bundle. Also, each Möb. (as well as corresponding operators) extended n>2. It there no - tuple operators B2(Dn) Aut(Dn), n>1. pairs B3(D2) Aut(D2) produced, it B3(Dn)