Some New Methods in the Theory of $m$-Quasi-Invariants

J. Bell, A. M. Garsia, N. Wallach
2005 Electronic Journal of Combinatorics  
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
more » ... so 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 fatcat:2r3hy3qu6zgj5kcucw2up3xt74