Let $\tilde{Gr}(k,n)$ be the affine cone of the Grassmannian $Gr(k,n)$. I think that the following set $S$ is an additive basis of $\mathbb{C}[\tilde{Gr}(k,n)]$: \begin{align} S = \{e_T: T \text{ is a rectangular semi-standard Young tableau with $k$ rows}\}, \end{align} where $e_T = P_{T_1} \cdots P_{T_n}$, where $T_i$'s are columns of $T$ and $P_{T_i}$ is the Pl"{u}cker with indices from the entries of $T_i$. Are there some references about this? Thank you very much.

Let $\tilde{Gr}(k,n)$ be the affine cone of the Grassmannian $Gr(k,n)$. I think that the following set $S$ is an additive basis of $\mathbb{C}[\tilde{Gr}(k,n)]$: \begin{align} S = \{e_T: T \text{ is a rectangular semi-standard Young tableau with $k$ rows}\}, \end{align} where $e_T = P_{T_1} \cdots P_{T_n}$, where $T_i$'s are columns of $T$ and $P_{T_i}$ is the Plücker with indices from the entries of $T_i$. Are there some references about this? Thank you very much.