Related papers: Low degree morphisms of E(5,10)-generalized verma …

Let $\mathfrak{g}$ be a classical complex simple Lie algebra and $\mathfrak{q}$ be a parabolic subalgebra. Generalized Verma module $M$ is called a scalar generalized Verma module if it is induced from a one-dimensional representation of…

The Lie algebra $sl_2 ( \mathbb{C} )$ may be regarded in a natural way as a subalgebra of the infinite-dimensional Virasoro Lie algebra, and this suggests there may be connections between the representation theory of the two algebras. In…

The aim of this work is to prove a technical result, that had been stated by Boyallian, Kac and Liberati \cite{ck6}, on the degree of singular vectors of finite Verma modules over the exceptional Lie superalgebra $E(1,6)$ that is isomorphic…

We classify and explicitly construct the embedding diagrams of Verma modules over the N=2 supersymmetric extension of the Virasoro algebra. The essential ingredient of the solution consists in drawing the distinction between two different…

We consider one of the most natural extended affine Lie lagebras, the algebra $sl_2({\mathbb C}_q)$ and begin a theory of its representations. In particular, we study a class of imaginary Verma modules, obtain a criterion of irreducibility…

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that…

We consider the principal subspaces of certain level $k\geqslant 1$ integrable highest weight modules and generalized Verma modules for the untwisted affine Lie algebras in types $D$, $E$ and $F$. Generalizing the approach of G. Georgiev we…

For any grading by an abelian group $G$ on the exceptional simple Lie algebra $\mathcal{L}$ of type $E_6$ or $E_7$ over an algebraically closed field of characteristic zero, we compute the graded Brauer invariants of simple…

Global Weyl modules for generalized loop algebras $\lie g\tensor A$, where $\lie g$ is a simple finite dimensional Lie algebra and A is a commutative associative algebra were defined, for any dominant integral weight $\lambda$, by…

In this paper, we introduce a new infinite-dimensional Lie superalgebra $\mathcal{S}$ called the super extended Ovsienko--Roger algebra. This algebra is obtained by determining the annihilation superalgebra of the Lie conformal superalgebra…

Let $\mathfrak{g}$ be a classial Lie algebra and $\mathfrak{p}$ be a maximal parabolic subalgebra. Let $M$ be a generalized Verma module induced from a one dimensional representation of $\mathfrak{p}$. Such $M$ is called a scalar type…

We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible…

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…

We show that if a module M over a basic classical Lie superalgebra of type type I is simultaneously a Verma module with respect to some Borel \(\mathfrak b_1\) and a dual Verma module with respect to Borel \(\mathfrak b_2\), then M is…

We study some variants of Verma modules of basic Lie superalgebras obtained via changing Borel subalgebras. These allow us to demonstrate that the principal block of \(\mathfrak{gl}(1|1)\) is realized as (non-Serre) full subcategories of…

Lowest weight modules, in particular, Verma modules over the N = 1,2 super Schrodinger algebras in (1+1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed via explicitly constructed singular vectors.…

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…

The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…

A class of generalized Verma modules over sl(m+1) are constructed from simple highest weight gl(m)-modules. Furthermore, the simplicity criterion for these sl(m+1)-modules are determined and an equivalence between generalized Verma modules…