Bell, J.; Garsia, A. M.; Wallach, N. Some new methods in the theory of \(m\)-quasi-invariants. (English) Zbl 1130.13003 Electron. J. Comb. 11, No. 2, Research paper R20, 32 p. (2005). 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. MSC: 13A50 Actions of groups on commutative rings; invariant theory 05E05 Symmetric functions and generalizations PDFBibTeX XMLCite \textit{J. Bell} et al., Electron. J. Comb. 11, No. 2, Research paper R20, 32 p. (2005; Zbl 1130.13003) Full Text: EuDML EMIS