Quasiinvariants of $S_3$

Details Quasiinvariants of $S_3$ Quasiinvariants of $S_3$

2006-03-20

arxiv.org/abs/math/0603482v1

J. Combin. Theory Ser. A 109 (2005), no. 2, 281--298

Mathematics

Combinatorics

18 pages, 2 figures, presented at 2004 Joint Meetings of the AMS and MAA

Scientific paper

Let $s_{ij}$ represent a tranposition in $S_n$. A polynomial $P$ in $\mathbb{Q}[X_n]$ is said to be $m$-quasiinvariant with respect to $S_n$ if $(x_i-x_j)^{2m+1}$ divides $(1-s_{ij})P$ for all $1 \leq i, j \leq n$. We call the ring $m$-quasiinvariants $QI_m[X_n]$. We describe a method for constructing a basis for the quotient $QI_m[X_3]/< e_1, e_2, e_3>$. This leads to the evaluation of certain binomial determinants that are interesting in their own right.

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