Related papers: Classification of simple Harish-Chandra modules ov…
In this paper, using the theory of $\A$-cover developed in \cite{B1,BF1}, we completely classify all simple Harish-Chandra modules over the high rank $W$-algebra $W(2,2)$. As a byproduct, we obtain the classification of simple…
In this paper, we classify simple Harish-Chandra modules over simple generalized Witt algebras.
In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra $W(\varrho)[s]$ for $s=0,\frac12$.…
We obtain a classification of simple modules with finite weight multiplicities over basic classical map superalgebras. Any such module is parabolic induced from a simple cuspidal bounded module over a cuspidal map superalgebra. Further on,…
In this paper, we classify the simple Harish-Chandra modules over the superconformal current algebra $\widehat{\frak g}$, which is the semi-direct sum of the $N=1$ superconformal algebra with the affine Lie superalgebra $\dot{\frak g}…
A notion of generalized highest weight modules over the high rank Virasoro algebras is introduced, and a theorem, which was originally given as a conjecture by Kac over the Virasoro algebra, is generalized. Mainly, we prove that a simple…
If $\Gamma$ is a subalgebra of $A$, then an $A$-module is called a Harish-Chandra module if it is the direct sum of its generalized weight spaces with respect to $\Gamma$. In 1994, Drozd, Futorny, and Ovsienko defined a generalization of a…
Let G be a nonlinear double cover of the real points of a connected reductive complex algebraic group with simply laced root system. We establish a uniform character multiplicity duality theory for the category of Harish-Chandra modules for…
Let $G$ be a semisimple algebraic group over the complex numbers and $K$ be a connected reductive group mapping to $G$ so that the Lie algebra of $K$ gets identified with a symmetric subalgebra of $\mathfrak{g}$. So we can talk about…
In this paper, we classify all simple jet modules for the Neveu-Schwarz algebra $\widehat{\mathfrak{k}}$ and its contact subalgebra $\mathfrak{k}^+$. Based on these results, we give a classification of simple Harish-Chandra modules for…
We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FuZ,RZ,Har]. The algebras are defined via a geometric realization in terms…
With the $\Omega$-operators for the Virasoro algebra \cite{BF} and the super Virasoro algebra in \cite{CL, CLL}, we get the $\Omega$-operators for the Ovsienko-Roger superalgebras in this paper and then use it to classify all simple…
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…
This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of…
In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra $W_{m,n}$ of vector fields on $\C^{m|n}$. Any such module is the unique simple submodule of some tensor module $F(P,V)$ for a simple weight module $P$…
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 simple Harish-Chandra modules over the super affine-Virasoro algebra $\widehat{\mathcal{L}}=\mathcal{W}\ltimes(\mathfrak{g}\otimes \mathcal{A})\oplus \mathbb{C}C$, where $\mathcal{A}=\mathbb{C}[t^{\pm…
For any reductive Lie algebra $\mathfrak{g}$ and commutative, associative, unital algebra $S$, we give a complete classification of the simple weight modules of $\mathfrak{g}\otimes S $ with finite weight multiplicities. In particular, any…
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 use Block's classification of simple modules over the first Weyl algebra to obtain a complete classification of simple weight modules, in particular, of Harish-Chandra modules, over the 1-spatial ageing algebra age(1). Most…