5 problems

Let $n$ and $k$ be integers satisfying $1\leq k<k+1\leq n-k$, and let $\mathfrak{a}(n+1,j+1,j+1)$ denote the Specht ideal associated with the partition $(n+1,j+1,j+1)$. Perfection…

Fix a positive integer $n$, a field ${\mathbb F}$, and let $R={\mathbb F}[x_1,\ldots,x_n]$. For a partition $\lambda\vdash n$, let $\mathfrak{a}(\lambda)$ denote the Specht ideal g…

Let $K$ be a field, let $R=K[x_1,\ldots,x_{2a+1}]$, and let $I^{\rm Sp}_{(a,a,1)}$ be the Specht ideal associated to the partition $(a,a,1)$. Linear-resolution conjecture. If … the…

Let $K$ be a field, let $R=K[x_1,\ldots,x_n]$, and let $\lambda=(\lambda_1,\ldots,\lambda_l)$ be a partition of $n$ satisfying condition (2) or (3) of the stated classification pro…

Let $K$ be a field, let $R=K[x_1,\ldots,x_n]$, and let $I^{\rm Sp}_\lambda$ denote the Specht ideal associated to a partition $\lambda$ of $n$. Radicality conjecture. The Specht id…