On the \(\mathcal S_{n}\)-modules generated by partitions of a given shape

Daniel Kane ; Steven Sivek

The electronic journal of combinatorics, Tome 15 (2008)

Résumé

Given a Young diagram $\lambda$ and the set $H^{\lambda}$ of partitions of $\{1,2,\dots$, $|\lambda|\}$ of shape $\lambda$, we analyze a particular ${\cal S}_{|\lambda|}$-module homomorphism ${\Bbb Q}H^{\lambda}\to{\Bbb Q}H^{\lambda'}$ to show that ${\Bbb Q}H^{\lambda}$ is a submodule of ${\Bbb Q}H^{\lambda'}$ whenever $\lambda$ is a hook $(n,1,1,\dots,1)$ with $m$ rows, $n\geq m$, or any diagram with two rows.

Détail

DOI : 10.37236/835

Classification : 05E10
Mots-clés : Young diagram, diagram with two rows