Very strong linkage for cohomology groups of line bundles on G/B
The author generalizes the strong linkage principle [the reviewer, J. Reine Angew. Math. 315, 53-59 (1980; Zbl 0439.20026)] for cohomology modules of line bundles on G/B. Here G is a reductive algebraic group over a field of positive characteristic and B is a Borel subgroup. The generalization gives for two p-singular weights \(\lambda\) and \(\mu\) a stronger necessary condition for the simple G-module with highest weight \(\lambda\) to occur as a composition factor in the cohomology of the line bundle on G/B induced by \(\lambda\). The paper also contains an infinitesimal version of the same principle. Recently, \textit{S. Doty} [in a preprint from Loyola Univ. Chicago (1987) entitled, The Strong Linkage Principle] has obtained similar results by starting out with the infinitesimal case and then deducing the principle for G.
scientific article; zbMATH DE number 4051886