  In this note, we study the polynomial representation of the quantum
Olshanetsky-Perelomov system for a finite reflection group $W$ of type $B_n$.
We endow the polynomial ring ${\mathbb C} [x_1,\ldots\\\ldots, x_n]$ with a
structure of module over the Weyl algebra associated with the ring ${\mathbb C}
[x_1,\ldots,x_n]^{W}$ of invariant polynomials under a reflections group $W$ of
type $B_n$. Then we study the polynomial representation of the ring of
invariant differential operators under the reflections group $W$. We use the
group representation theory namely the higher Specht polynomials associated
with the reflection group $W$ and establish a decomposition of that structure
by providing explicitly the generators of the simple components.
