Kostant modules in blocks of category ${\mathcal O}_S$
Abstract
Description
In this paper the authors investigate infinite-dimensional representations $L$ in blocks of the relative (parabolic) category ${\mathcal O}_S$ 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.
25 pages, 2 tables, 6 figures, uses PSTricks; v.2: added Secs. 4 (BGG resolutions) and 7.5 (Minimal free resolutions), expanded Introduction
25 pages, 2 tables, 6 figures, uses PSTricks; v.2: added Secs. 4 (BGG resolutions) and 7.5 (Minimal free resolutions), expanded Introduction