Kostant Modules in Blocks of Category 𝒪S

In this article, the authors investigate infinite-dimensional representations L in blocks of the relative (parabolic) category 𝒪 S for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in L “looks like” the cohomology with coefficients in a finite-dimensional module, as in Kostant's theorem. A complete classification of these “Kostant modules” in regular blocks for maximal parabolics in the simply laced types is given. A complete classification is also given in arbitrary (singular) blocks for Hermitian symmetric categories.