Holomorphic representation of Olshanetsky-Perelomov operators associated with the Weyl group of type Bn.

In this paper, we study the holomorphic representation of Olshanetsky-Perelomov operators associated with the weyl group W of type Bn. Thus, we view the algebra ℋ (ℂn) of holomorphic functions as a module the ring 풟 of invariant differential operators under the group W. Then we study the holomorphic representation of 풟. Using the representation theory of the Weyl group W, we construct the irreducible components of ℋ (ℂn), by explicity providing their generators. [ABSTRACT FROM AUTHOR]