Related papers: Classification of Harish-Chandra modules over the …
Let $G$ be a rank $n$ additive subgroup of $\bC$ and $\Vir[G]$ the corresponding Virasoro algebra of rank $n$. In the present paper, irreducible weight modules with finite dimensional weight spaces over $\Vir[G]$ are completely determined.…
It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains…
Characteristic cycles and leading term cycles of irreducible highest weight Harish-Chandra modules of regular integral infinitesimal character are determined. In the simply laced cases they are irreducible, but in the nonsimply laced cases…
A natural higher dimensional analogue of the affine-Virasoro algebra is the full toroidal Lie algebra. In this paper, we classify irreducible Harish-Chandra modules for map full toroidal Lie algebras. We show that every such module is…
In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.
We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$. We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$, which are…
We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We…
In this paper, we classify all simple weight modules with finite-dimensional weight spaces over the $N=2$ Ramond algebra. Any such module $V$ is either a simple highest weight module or a simple lowest weight module, or a simple cuspidal…
Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…
In this paper it is proved that an irreducible weight module with finite-dimensional weight spaces over the Schr\"{o}dinger-Virasoro algebras is a highest/lowest weight module or a uniformly bounded module. Furthermore, indecomposable…
We consider the category of Harish-Chandra modules for ${\rm SL}_2(\mathbb R)$ as a module over the category of finite-dimensional representations of ${\rm SL}(2)$ with respect to the tensor product. In this note we use classical results…
For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…
Verma modules over the $W$-algebra W(2,2) were considered by Zhang and Dong, while the Harish-Chandra modules and irreducible weight modules over the same algebra were classified by Liu and Zhu etc. In the present paper we shall investigate…
All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.
We prove that any irreducible Harish-Chandra modules for a class of Lie algebras, which we call gap-$p$ Virasoro algebras, must be a highest weight module, a lowest weight module, or a module of intermediate series.These algebras are…
We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step towards the classification of finite dimensional irreducible modules. Motivated by known results in type A, we…
In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebras $\mathcal{W}(b)$ with $b\in\mathbb{C}$ related to the Virasoro conformal algebra. Explicitly, any finite irreducible conformal module…
In this paper, we classify all irreducible weight modules with finite-dimensional weight spaces over the affine-Virasoro Lie algebra of type $A_1$.
In this paper, we classify the irreducible Harish-Chandra modules over the full toroidal Lie algebra, which is a natural higher-dimensional analogue of the affine-Virasoro algebra. In particular, we complete the classification of…
In this paper, we consider the classification of irreducible ${\bf Z}$- and ${\bf Z}^2$-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded…