Related papers: Whittaker modules over the loop Virasoro algebra

For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra $A$ of functions and the Lie algebra $\mathcal{V}$ of vector fields on the variety. We prove that a gauge…

This paper addresses the representation theory of the insertion-elimination Lie algebra, a Lie algebra that can be naturally realized in terms of tree-inserting and tree-eliminating operations on rooted trees. The insertion-elimination…

In this paper, by using the "twisting technique" we obtain a class of new modules $A_b$ over the Witt algebras $\mathcal{W}_n$ from modules $A$ over the Weyl algebras $\mathcal{K}_n$ (of Laurent polynomials) for any $b\in\mathbb{C}$. We…

Let $A_n=\mathbb{C}[t_i^{\pm1},~1\leq i\leq n]$ and $\mathbf{W}(n)_\mu=A_nd_\mu$ the solenoidal Lie algebra introduced by Y.Billig and V.Futorny in \cite{BiFu2}, where $\mu=(\mu_1,\ldots,\mu_n)\in\mathbb{C}^n$ is a generic vector and…

In the present paper, we construct two classes of non-weight modules $\Omega(\lambda,\alpha,\beta)\otimes\mathrm{Ind}(M)$ and $\mathcal{M}\big(V,\Omega(\lambda,\alpha,\beta)\big)$ over the twisted Heisenberg-Virasoro algebra, which are both…

We define a filtration of a standard Whittaker module over a complex semisimple Lie algebra and and establish its fundamental properties. Our filtration specialises to the Jantzen filtration of a Verma module for a certain choice of…

In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related…

We identify Whittaker vectors for $\mathcal{W}_k(\mathfrak{g})$-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable…

Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of…

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 $s=0,\frac12$.…

It is proved that uniformly bounded simple modules over higher rank super-Virasoro algebras are modules of the intermediate series, and that simple modules with finite dimensional weight spaces are either modules of the intermediate series…

For a basic classical Lie superalgebra $\mathfrak s$, let $\mathfrak g$ be the central extension of the Takiff superalgebra $\mathfrak s\otimes\Lambda(\theta)$, where $\theta$ is an odd indeterminate. We study the category of $\mathfrak…

We present the list of irreducible (generalized) highest weight modules over the Virasoro algebra and N=1 super-Virasoro algebras obtained as factor-modules of (generalized) Verma modules. We present also the character formulae of all these…

In this paper, we study irreducible weight modules with infinite dimensional weight spaces over the mirror-twisted Heisenberg-Virasoro algebra $\mathcal{D}$. More precisely, the necessary and sufficient conditions for the tensor products of…

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 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…

For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$ of $\hat{\mathfrak{g}}$, we prove that certain subcategory of weak $V_k(\mathfrak{g})$-module category is semisimple. As a consequence, we show that…

By using methods developed in arXiv:math/0602181 we study the irreducibility of certain Wakimoto modules for $\widehat{sl_2}$ at the critical level. We classify all $\chi \in {\Bbb C}((z))$ such that the corresponding Wakimoto module…

For any $n\in \mathbb{Z}_{\geq 2}$, let $\mathfrak{m}_n$ be the subalgebra of $\mathfrak{sp}_{2n}$ spanned by all long negative root vectors $X_{-2\epsilon_i}$, $i=1,\dots,n$. An $\mathfrak{sp}_{2n}$-module $M$ is called a Whittaker module…

Irreducibilities of Verma modules over a class of Block type Lie algebras are completely determined. The approach developed in the present paper can be used to deal with non-weight modules.