Related papers: Annihilators of simple integrable weight $\mathfra…

We classify integrable bounded simple weight modules over classical Lie superalgebras at infinity. We also study the categories of such modules, and we prove that for most of the classical Lie superalgebras at infinity the respective…

This paper is concerned with weak* closed masa-bimodules generated by A(G)-invariant subspaces of VN(G). An annihilator formula is established, which is used to characterise the weak* closed subspaces of B(L^2(G)) which are invariant under…

We show how to compute annihilators and associated varieties of simple Harish-Chandra modules for Sp(p,q) with trivial infinitesimal character from a pair of domino tableaux attached to a parameter for such a module.

For the algebra $I_n$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple weight and generalized weight (left and right) $I_n$-modules is given. It is proven that the category of…

It is proved that an irreducible quasifinite $W_\infty$-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight $W_\infty$-module is a module of the intermediate series.…

Let $R$ be a commutative Noetherian ring, $\mathfrak a$ a proper ideal of $R$ and $N$ a non-zero finitely generated $R$-module with $N\neq \mathfrak a N$. Let $d$ (respectively $c$) be the smallest (respectively greatest) non-negative…

In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules $L$ over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras $\mathfrak{g}$. The problems…

Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of…

Let $\fg$ be any untwisted affine Kac-Moody algebra, $\mu$ any fixed complex number, and $\wt\fg(\mu)$ the corresponding toroidal extended affine Lie algebra of nullity two. For any $k$-tuple $\bm{\lambda}=({\lambda}_1, \cdots,…

A weight $\mathfrak{sl}_{n+1}$-module with finite-dimensional weight spaces is called a cuspidal module, if every root vector of $\mathfrak{sl}_{n+1}$ acts injectively on it. In \cite{LL}, it has been shown that any block with a generalized…

Using simple modules over the derivation Lie algebra $C[t]\frac{d}{d t}$ of the associative polynomial algebra $C[t]$, we construct new weight Virasoro modules with all weight spaces infinite dimensional. We determine necessary and…

We show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde\goth g$ we construct the corresponding level $k$ vertex operator algebra and we show that level $k$ highest weight $\tilde\goth…

In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…

This work provides the first step toward the classification of irreducible finite weight modules over twisted affine Lie superalgebras. We study all such modules whether the canonical central element acts as a nonzero multiple of the…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

Permutation modules are fundamental in the representation theory of symmetric groups $\Sym_n$ and their corresponding Iwahori--Hecke algebras $\He = \He(\Sym_n)$. We find an explicit combinatorial basis for the annihilator of a permutation…

Given an arbitrary sheaf $\mathcal{E}$ of $\mathcal{A}$-modules (or $\mathcal{A}$-module in short) on a topological space $X$, we define \textit{annihilator sheaves} of sub-$\mathcal{A}$-modules of $\mathcal{E}$ in a way similar to the…

Let g_A (respectively, g_A(\mu)) be the graded multi-loop Lie algebra (respectively graded twisted multi-loop Lie algebra)" associated with the simple finite dimensional Lie algebra g over the complex field C. In this paper, we prove that…

An $A$-module $E$ is said to be an \textit{annihilator multiplication module} if for each $e\in E$, there exists a finitely generated ideal $I$ of $A$ such that $ann(e)=ann(IE)$. This class of modules is quite large, as it contains…

We provide a micro-local necessary condition for distinction of admissible representations of real reductive groups in the context of spherical pairs. Let $\bf G$ be a complex algebraic reductive group, and $\bf H\subset G$ be a spherical…