Some new methods in the Theory of m-Quasi-Invariants

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Some new methods in the Theory of m-Quasi-Invariants

We introduce here a new approach to the study of m-quasi-invariants. This approach consists in representing m-quasi-invariants as N tuples of invariants. Then conditions are sought which characterize such N tuples. We study here the case of S3 m-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions e1,e2,e3 which explains certain observed properties of S3 m-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of Sn m-quasi-invariants