Holomorphic representation of the Calogero-Moser system.

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]