Some new methods in the theory of \(m\)-quasi-invariants (Q2570989)

Summary: 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 \(S_3\) \(m\)-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions \(e_1,e_2,e_3\), which explains certain observed properties of \(S_3\) \(m\)-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of \(S_n\) \(m\)-quasi-invariants.