Quasi-invariant and super-coinvariant polynomials for the generalized symmetric group
| 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 | The aim of this work is to extend the study of super-coinvariant polynomials, to the case of the generalized symmetric group $G_{n,m}$, defined as the wreath product $C_m\wr§_n$ of the symmetric group by the cyclic group. We define a quasi-symmetrizing action of $G_{n,m}$ on $\Q[x_1,...,x_n]$, analogous to those defined by Hivert in the case of $§_n$. The polynomials invariant under this action are called quasi-invariant, and we define super-coinvariant polynomials as polynomials orthogonal, with respect to a given scalar product, to the quasi-invariant polynomials with no constant term. Our main result is the description of a Gröbner basis for the ideal generated by quasi-invariant polynomials, from which we dedece that the dimension of the space of super-coinvariant polynomials is equal to $m^n C_n$ where $C_n$ is the $n$-th Catalan number. | |
| dc.identifier | https://arxiv.org/abs/0711.0908 | |
| dc.identifier | http://arxiv.org/abs/0711.0908 | |
| dc.identifier | Formal Power Series and Algebraic Combinatorics, Linköping : Suède (2003) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141557 | |
| dc.subject | Combinatorics | |
| dc.title | Quasi-invariant and super-coinvariant polynomials for the generalized symmetric group | |
| dc.type | text |