On extensions of hook Weyl modules

We determine the integral extension groups $Ex{t}^1(\mathrm{\Delta }(h),\mathrm{\Delta }(h(k)))$ and $Ex{t}^k(\mathrm{\Delta }(h),\mathrm{\Delta }(h(k)))$, where $\mathrm{\Delta }(h),\mathrm{\Delta }(h(k))$ are the Weyl modules of the general linear group $G{L}_n$ corresponding to the hook partitions $h=(a,1^b)$, $h(k)=(a+k,1^{b-k})$.