On the irreducibility of a class of homogeneous operators

Abstract

In this paper we construct a class of homogeneous Hilbert modules over the disc algebra $\mathcal{A}(\mathbb{D})$ as quotients of certain natural modules over the function algebra $\mathcal{A}({\mathbb{D}}^2)$. These quotient modules are described using the jet construction for Hilbert modules. We show that the quotient modules obtained this way, belong to the class ${\mathrm{B}}_k(\mathbb{D})$ and that they are mutually inequivalent, irreducible and homogeneous.