Schubert filtration for simple quotients of generalized Verma modules

Generalized Verma Modules

On multiplicities of simple subquotients in Generalized Verma modules

We reduce the problem on multiplicities of simple subquotients in an-stratiied Generalized Verma module to the analogous problem for classical Verma modules.

Closed Product Formulas for Extensions of Generalized Verma Modules

We give explicit combinatorial product formulas for the polynomials encoding the dimensions of the spaces of extensions of (g, p)-generalized Verma modules, in the cases when (g, p) corresponds to an indecomposable classic Hermitian symmetric pair. The formulas imply that these dimensions are combinatorial invariants. We also discuss how these polynomials, defined by Shelton, are related to the...

Systems of Differential Operators and Generalized Verma Modules

In this paper we close the cases that were left open in our earlier works on the study of conformally invariant systems of second-order differential operators for degenerate principal series. More precisely, for these cases, we find the special values of the systems of differential operators, and determine the standardness of the homomorphisms between the generalized Verma modules, that come fr...

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 (