Polynômes quasi-invariants et super-coinvariants pour le groupe symétrique généralisé
| dc.creator | Aval, Jean-Christophe | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:41:03Z | |
| dc.date.available | 2026-07-07T08:41:03Z | |
| dc.description | A classical result of Artin states that the ideal generated by symmetric polynomials in $n$ variables is of codimension $n!$. The author, F. Bergeron and N. Bergeron have recently obtained a surprising analogous in the case of quasi-symmetric polynomials. In this case, the ideal is of codimension given by $C_n$, the $n$-th Catalan number. Quasi-symmetric polynomials are the invariants of a certain action of the symmetric group $S_n$ defined by F. Hivert. The aim of this work is to generalize these results to the wreath product $S_n\wr \Z_m$, also known as the generalized symmetric group $G\nm$. We first define a quasi-symmetrizing action of $G\nm$ on $\C[x_1,...,x_n]$, then obtain a description of the invariants and the codimension of the associated ideal, which is $m^n C_n$. | |
| dc.identifier | https://arxiv.org/abs/0711.0909 | |
| dc.identifier | http://arxiv.org/abs/0711.0909 | |
| dc.identifier | Annales des sciences mathématiques du Québec 27, 2 (2003) 111-121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141558 | |
| dc.subject | Combinatorics | |
| dc.title | Polynômes quasi-invariants et super-coinvariants pour le groupe symétrique généralisé | |
| dc.type | text |