Structure of cohomology modules of linear bundles over \(G/B\)
Let \(G\) be a connected, simply connected semi-simple algebraic group over an algebraically closed field of positive characteristic, and let \(B \subset G\) be a Borel subgroup. The author studies the representation of \(G\) on the cohomology of line bundles over the homogenenous space \(G/B\) defined by certain characters of \(B\). He obtains submodules and quotient modules of these \(G\)-modules. The results generalize work of \textit{J. E. Humphreys} [Commun. Algebra 12, 2665-2677 (1984; Zbl 0546.20036)] on the structure of Weyl modules.
scientific article; zbMATH DE number 1256788