A family of homogeneous operators in the Cowen–Douglas class over the poly-disc

Abstract

We construct a large family of positive definite kernels $K: \mathbb D^n\times \mathbb D^n \to \mathrm M (r, \mathbb C)$, holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the subgroup Möb$\,\ti