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In this note, we study the action of the Calogero-Moser system on the algebra ℋ (ℂn)of holomorphic functions over ℂn. We consider the algebra 풟 of invariant differential operators with analytic coefficients under the symmetric group and its representation on ℋ (ℂn). We provide the irreducible decomposition of ℋ (ℂn) as a module over 풟. We explicitly describe the irreducible component by giving it generators. [ABSTRACT FROM AUTHOR]

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]