I heard someone said( maybe Okonov) that specht module is the intersection of two induced modules, but I do not know why.The details of my question is as follows.

Let $\lambda\vdash n$ be a partiton, the specht module $S^\lambda$ is the irreducible module of $S_n$ corresponding to the partition $\lambda$.

I guess (of course maybe I'm wrong) that $S^\lambda$ can be obtained as follows: define $$R=S_{\{1,\ldots,\lambda_1\}}\times S_{\{\lambda_1+1,\ldots,\lambda_1+\lambda_2\}}\times\cdots$$ be the Young subgroup with respect to $\lambda$, and $$C=S_{\{1,\ldots,\lambda_1'\}}\times S_{\{\lambda_1'+1,\ldots,\lambda_1'+\lambda_2'\}}\times\cdots$$ be the Young subgroup with respect to the conjugate partition $\lambda'$(transpose of $\lambda$).

Assertion： $S^\lambda$ is the intersection of $\text{Ind}_{1_R}^{S_n}$ and $\text{Ind}_{1_c\otimes\epsilon}^{S_n}$. where $\epsilon$ is the 1-dimensional sign representation of $C$.

I know the tabloid - polytabloid approach of constructing specht modules, but I wonder whether this way is equivalent to the construction depicted above.Can anyone explain me the connections? thanks.