Socles of Verma modules in quantum groups

Semi–holonomic Verma Modules

Verma modules arise geometrically through the jets of homogeneous vector bundles. We consider in this article, the modules that arise from the semi-holonomic jets of a homogeneous vector bundle. We are particularly concerned with the case of a sphere under MMbius transformations. In this case there are immediate applications in the theory of conformally invariant diierential operators.

Quantum coadjoint orbits of GL(n) and generalized Verma modules

In our previous paper, we constructed an explicit GL(n)-equivariant quantization of the Kirillov–Kostant-Souriau bracket on a semisimple coadjoint orbit. In the present paper, we realize that quantization as a subalgebra of endomorphisms of a generalized Verma module. As a corollary, we obtain an explicit description of the annihilators of generalized Verma modules over U (

Generalized Verma Modules

Socles of Buchsbaum modules, complexes and posets

The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative Kühnel’s conjecture ...

Twisted Verma modules

Using principal series Harish-Chandra modules, local cohomology with support in Schubert cells and twisting functors we construct certain modules parametrized by the Weyl group and a highest weight in the subcategory O of the category of representations of a complex semisimple Lie algebra. These are in a sense modules between a Verma module and its dual. We prove that the three different approa...