  Let $\Omega$ be an irreducible bounded symmetric domain of rank $r$ in
$\mathbb C^d.$ Let $\mathbb K$ be the maximal compact subgroup of the identity
component $G$ of the biholomorphic automorphism group of the domain $\Omega$.
The group $\mathbb K$ consisting of linear transformations acts naturally on
any $d$-tuple $\boldsymbol T=(T_1,\ldots, T_d)$ of commuting bounded linear
operators. If the orbit of this action modulo unitary equivalence is a
singleton, then we say that $\boldsymbol T$ is $\mathbb{K}$-homogeneous. In
this paper, we obtain a model for all $\mathbb{K}$-homogeneous $d$-tuple
$\boldsymbol{T}$ as the operators of multiplication by the coordinate functions
$z_1,\ldots ,z_d$ on a reproducing kernel Hilbert space of holomorphic
functions defined on $\Omega$. Using this model we obtain a criterion for (i)
boundedness, (ii) membership in the Cowen-Douglas class (iii) unitary
equivalence and similarity of these $d$-tuples. In particular, we show that the
adjoint of the $d$-tuple of multiplication by the coordinate functions on the
weighted Bergman spaces are in the Cowen-Douglas class $B_1(\Omega)$. For a
bounded symmetric domain $\Omega$ of rank $2$, an explicit description of the
operator $\sum_{i=1}^d T_i^*T_i$ is given. In general, based on this formula,
we make a conjecture giving the form of this operator.
