Schur algebras of reductive p-adic groups, I

Abstract

We give a link–through the affine Schur algebra–between the representations of the $p$-affine Schur algebra of ${\rm GL}(n)$ over $R$ and the smooth $R$-representations of the $p$-adic group ${\rm GL}(n,\mathbf {Q}\sb p)$ over any algebraically closed field $R$ of characteristic not equal to $p$.