Geodesic
Some new methods in the theory of \(m\)-quasi-invariants
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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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
DOI : 10.37236/1877
Classification : 13A50, 05E05 
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     author = {J. Bell and A. M. Garsia and N. Wallach},
     title = {Some new methods in the theory of \(m\)-quasi-invariants},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1877},
     zbl = {1130.13003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1877/}
}
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J. Bell; A. M. Garsia; N. Wallach. Some new methods in the theory of \(m\)-quasi-invariants. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1877

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