Submodule Structure of Generalized Verma Modules Induced from Generic Gelfand-Zetlin Modules

For complex Lie algebra sl(n, C) we study the submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules over some subalgebra of type sl(k, C). We obtain necessary and sufficient conditions for the existence of a submodule generalizing the Bernstein-Gelfand-Gelfand theorem for Verma modules.     

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.      

On the Reducibility of Scalar Generalized Verma Modules of Abelian Type

A parabolic subalgebra \(\mathfrak {p}\) of a complex semisimple Lie algebra \(\mathfrak {g}\) is called a parabolic subalgebra of abelian type if its nilpotent radical is abelian. In this paper, we provide a complete characterization of the parameters for scalar generalized Verma modules attached to parabolic subalgebras of abelian type such that the modules are reducible. The proofs use Jantzen’s simplicity criterion, as well as the Enright-Howe-Wallach classification of unitary highest weight modules.     

Verma Modules Over Generalized Block Algebras B(b (1), b (2))

ABSTRACT

Given a field F with characteristic zero, a free Abelian group G with rank two, and a total order ? on G which is compatible with the addition, we define Verma modules M([ddot], ?) over the generalized Block algebra B(b ⁽¹⁾, b ⁽²⁾) with b ⁽¹⁾, b ⁽²⁾ ∈ F. The irreducibility of the module M([ddot], ?) is completely determined in this article.     

某些$W$-型李代数的Verma模

本文我们研究了两类$W$-型李代数$g(\lambda)$的Verma模的结构. 在一定条件下,我们决定了这些Verma模的可约性及相应的奇异向量.     

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 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.     

Verma type modules of level zero for affine Lie algebras

We study the structure of Verma type modules of level zero induced from non-standard Borel subalgebras of an affine Kac-Moody algebra. For such modules in ``general position' we describe the unique irreducible quotients, construct a BGG type resolution and prove the BGG duality in certain categories. All results are extended to generalized Verma type modules of zero level.

     

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.     

On Gelfand-Kirillov Transcendence Degree

We study some basic properties of the Gelfand-Kirillov transcendence degree and compute the transcendence degree of various infinite-dimensional division algebras including quotient division algebras of quantized algebras related to quantum groups, 3-dimensional Artin-Schelter regular algebras and the 4-dimensional Sklyanin algebra.

     

Gelfand-Kirillov dimension in Jordan Algebras

In this paper we study Gelfand-Kirillov dimension in Jordan algebras. In particular we will relate Gelfand-Kirillov (GK for short) dimensions of a special Jordan algebra and its associative enveloping algebra and also the GK dimension of a Jordan algebra and the GK dimension of its universal multiplicative enveloping algebra.

     

Fock Space Realizations of Imaginary Verma Modules

This work expands to the setting of the results of H. Jakobsen and V. Kac and independently D. Bernard and G. Felder on the realization of , in terms of infinite sums of partial differential operators. We note in the paper that, in the generic case, these geometric constructions are just realizations of the imaginary Verma modules studied by V. Futorny. Presented by A. VerschorenMathematics Subject Classifications (2000) Primary: 17B67, 81R10.     

广义Macaulay-Northcott模与Tor-群

Let （S,≤） be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups：Tori[[ RS,≤]]（[[MS,≤]],[NS,≤]）≌ s∈S ToriR （M,N）.     

弱总体维数和模的自同态

本文用模的自同态,给出弱总体维数≤ｎ的环的特征,其中ｎ≥０．设Ｒ为环,部分地回答了下列问题：何时任意有限表现Ｒ－模Ｍ有无穷分解：０→Ｍ→Ｆ₀→Ｆ₁→…→Ｆ_n→…,其中每个Ｆ_i均是有限生成投射的,ｉ＝１,２,…？     

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.     

带三角分解李代数的赋值模

设F是特征零的域，L是F上的带三角分解的李代数，L^-是相应的Loop代数．本文将定义L^-上赋值模的概念，并给出其不可约模的张量积是不可约模的等价条件．     

Weak Dimension of FP-injective Modules Over Chain Rings

It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2. This implies that the projective dimension of any countably generated FP-injective module over an Archimedean chain ring is less or equal to 3.     

A result on the Gelfand-Kirillov dimension of representations of classical groups

Let be the reductive dual pair . We show that if is a representation of (respectively ) obtained from duality correspondence with some representation of (respectively ), then its Gelfand-Kirillov dimension is less than or equal to
(respectively ).