Homogeneous analytic Hilbert modules -- the case of non-transitive action

This work investigates analytic Hilbert modules $\mathcal{H}$, over the polynomial ring, consisting of holomorphic functions on a $G$-space $Ω\subset \mathbb{C}^m$ that are homogeneous under the natural action of the group $G$. In a departure from the past studies of such questions, here we don't as