Schur and Weyl modules.

Question

Let $m$ be a non-negative integer and $\lambda=(\lambda_1, \cdots, \lambda_s)$ a partition of $m$. If $V$ is a vector space of dimension $n$ (over a field $\mathbb{K}$), we can consider the Schur module $L_{\lambda}E$ and the Weyl module $K_\lambda E$. How can I prove that if the characteristic of the field $\mathbb{K}$ is $0$, then $ K_\lambda E $ is isomorphic to $L_{\lambda '}E $, where $\lambda'$ is the dual partition? Thank you.