Determining maximal Cohen-Macaulay modules over an invariant ring

Question

Suppose that $G$ is a finite small (i.e. reflection-free) subgroup of $\text{GL}(n,\mathbb{C})$ acting on $S := \mathbb{C}[x_1, \dots, x_n]$. Set $R := S^G$. By 5.20 Corollary of this, the maximal Cohen Macaulay modules of $R$ are in bijection with the irreps of $G$ and are given by $M_j := (S \otimes_\mathbb{C} V_j)^G$, where $V_j$ is the $j$th irrep. If $V_j$ is one dimensional with corresponding character $\chi_j$, then $M_j$ is isomorphic to \begin{align*} \{ f \in S \mid g \cdot f = \chi_j(g)^{-1} f \text{ for all } g \in G \}. \end{align*} Is there a similar description of the maximal Cohen-Macaulay module $M_j$ when $V_j$ has dimension 2 or greater? Preferably one which only relies on knowing the character, and not requiring one to construct the corresponding representation explicitly.