Differential operators and reection group of type Bn

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