The structure of Humphreys-Verma modules for projective spaces
Let \(E\) be a finite dimensional linear space over an algebraically closed field \(\mathbf k\) of positive characteristic, \(G=\text{GL}(E)\), and \(P\) a parabolic subgroup of \(G\) such that \(G/P\) is a projective space over \(\mathbf k\). Let \(G_1\) be the Frobenius kernel of \(G\) and \(T\) a maximal torus of \(P\). The author determined the \(G_1T\)-structure on all \(G_1P\)-modules induced from \(1\)-dimensional \(P\)-modules. They are all multiplicity-free and uniserial.
scientific article; zbMATH DE number 5602650