Kostant modules in blocks of category \mathcal O_S

2006/04/14 by Brian D. Boe, Boe, Brian D., Markus Hunziker +1
Mathematics · #17B10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0604336

openalex publication_date 2006/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Kostant's problem for parabolic Verma modules
• Cohomology in singular blocks of parabolic category O
• Almost all permutations and involutions are Kostant negative
• Kostant's problem and parabolic subgroups
• Projective modules over classical Lie algebras of infinite rank in the parabolic category