Bases explicites et conjecture n!
Abstract
Description
The aim of this work is to construct a monomial and explicit basis for the space $M_μ$ relative to the $n!$ conjecture. We succeed completely for hook-shaped partitions, i.e. $μ=(K+1,1^L)$. We are indeed able to exhibit a basis and to verify that its cardinality is $n!$, that it is linearly independent and that it spans $M_μ$. We deduce from this study an explicit and simple basis for $I_μ$, the annulator ideal of $Δ_μ$. This method is also successful for giving directly a basis for the homogeneous subspace of $M_μ$ consisting of elements of 0 $x$-degree.