On extensions of hook Weyl modules

Abstract

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