Reducibility of generalized Verma modules for Hermitian symmetric pairs

In this article, we give some practical criteria to determine the reducibility of generalized Verma modules (induced from finite-dimensional modules) in the Hermitian symmetric case. Our criteria are given by the information of the corresponding highest weights of the finite-dimensional modules and relatively easy to verify. This article is inspired by earlier work of Kubo about Jantzen's criterion.     

Extensions between generalized Verma modules: The Hermitian symmetric cases

Supported in part by NSF postdoctoral fellowship # DMS-8414100     

Verma modules over generalized Witt algebras

We constuct and investigate a structure of Verma-like modules over generalized Witt algebras. We also prove Futorny-like theorem for irreducible weight modlues whose dimensions of the weight spaces are uniformly bounded.     

Intertwining differential operators and reducibility of generalized Verma modules

Supported in part by NSF Grant DMS-8610730     

On multiplicities of simple subquotients in generalized Verma modules

We reduce the problem on multiplicities of simple subquotients in an -stratified 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 -generalized Verma modules, in the cases when 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 parabolic -polynomials introduced by Deodhar.

     

Verma modules over generalized Virasoro algebras Vir[G]

Let F be a field of characteristic 0, not necessarily algebraically closed, and G be an additive subgroup of F. For any total order on G which is compatible with the group addition, and for any , a Verma module over the generalized Virasoro algebra Vir[G] is defined. In the present paper, the irreducibility of Verma modules is completely determined.     

Verma modules for twisted Yangians

Abstract

A sufficient and necessary condition for the reducibility of the Verma modules over the twisted Yangians of rank one is given.     

Generalized imaginary Verma and Wakimoto modules

We develop a general technique of constructing new irreducible weight modules for any affine Kac-Moody algebra using the parabolic induction, in the case when the Levi factor of a parabolic subalgebra is infinite-dimensional and the central charge is nonzero. Our approach unifies and generalizes all previously known results with imposed restrictions on inducing modules. We also define generalized imaginary Wakimoto modules which provide an explicit realization for generic generalized imaginary Verma modules.     

Verma type modules for toroidal lie algebras

We study the structure of imaginary Verma modules induced from the"natural"Borel subalgebra of a toroidal Lie algebra. In particular, we establish a criterion of irreducibility for imaginary Verma modules and describe their submodules and irreducible quotients. We also describe the structure of Verma type modules in the case of sl(2)-toroidal Lie algebra over two variables.     

Verma modules for rank two Heisenberg-Virasoro algebra

Let■ be a compatible total order on the additive group Z~2,and L be the rank two HeisenbergVirasoro algebra.For any c=(c_1,c_2,c_3,c_4) ∈ C~4,we define a Z~2-graded Verma module M(c,■) for L.A necessary and sufficient condition for M(c,■) to be irreducible is provided.Moreover,the maximal Z~2-graded submodules of M(c,■) are characterized when M(c,■) is reducible.     

Generalized Verma modules over some Block algebras

In this paper, a class of generalized Verma modules M(V) over some Block type Lie algebra ℬ(G) are constructed, which are induced from nontrivial simple modules V over a subalgebra of ℬ(G). The irreducibility of M(V) is determined.      

Special vectors in Verma modules over affine algebras

M. V. Lomonosov Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 23, No. 1, pp. 76–77, January–March, 1989.     

Structure of certain Verma modules over affine Lie algebras

Moscow Institute of Electronics Engineering. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 4, pp. 82–83, October–December, 1990.