The Subnormality of $\mathbb{K}$-Homogeneous Multiplication Operators on Bounded Symmetric Domains

Let $\mathrm{\Omega }=G\mathrm{/}\mathbb{K}$ be an irreducible bounded symmetric domain of rank $r$ and dimension $d\mathrm{.}$ In this paper, we study the joint subnormality of $d$-tuple of multiplication operators induced by the coordinate functions on reproducing kernel Hilbert spaces of holomorphic functions on $\mathrm{\Omega }$ determined by $\mathbb{K}$-invariant kernels. We introduce the notion of contractive $d$-tuple associated with $\mathrm{\Omega }$ and prove that the weighted Bergman shifts on $\mathrm{\Omega }$ are contractive $d$-tuple precisely when they are jointly subnormal. A characterization of joint subnormality further leads to the study of a class of moment problems, which we refer to as twisted moment problems. We establish that the twisted moment problem is equivalent to an appropriate Hausdorff moment problem. This equivalence provides a moment-theoretic characterization of joint subnormality for the multiplication operators under consideration.