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In this paper we study the representations of loop Affine-Virasoro Algebras. As they have canonical triangular decomposition, we define Verma modules and its irreducible quotients. We give necessary and sufficient condition for an…

Representation Theory · Mathematics 2020-01-29 S. Eswara Rao

We study irreducible modules for map Heisenberg-Virasoro algebras. In particular, we give a complete classification of irreducible Harish-Chandra modules for map Heisenberg-Virasoro algebras. We will also classify non-weight irreducible…

Representation Theory · Mathematics 2023-11-07 Priyanshu Chakraborty

The loop-Virasoro algebra is the Lie algebra of the tensor product of the Virasoro algebra and the Laurent polynomial algebra. This paper classifies irreducible Harish-Chandra modules over the loop-Virasoro algebra, which turn out to be…

Representation Theory · Mathematics 2013-01-04 Xiangqian Guo , Rencai Lu , Kaiming Zhao

An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite dimensional weight spaces. Recently the irreducible integrable modules having…

Representation Theory · Mathematics 2021-01-13 Souvik Pal

In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where $q$ is a…

Representation Theory · Mathematics 2018-09-26 Qiu-Fan Chen , Yu-Feng Yao

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…

Representation Theory · Mathematics 2019-11-01 Chengkang Xu

Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loop-Virasoro algebra $Vir…

Representation Theory · Mathematics 2021-12-28 Priyanshu Chakraborty , Punita Batra

In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo,…

Representation Theory · Mathematics 2024-07-30 Qiu-Fan Chen , Yu-Feng Yao

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…

Representation Theory · Mathematics 2021-04-20 Dongfang Gao , Kaiming Zhao

We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional.…

Representation Theory · Mathematics 2010-04-02 Volodymyr Mazorchuk , Kaiming Zhao

In this paper, the conjugate-linear anti-involutions and the unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified respectively. We prove that any unitary irreducible module of…

Rings and Algebras · Mathematics 2012-01-09 Xiufu Zhang , Shaobin Tan

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…

Representation Theory · Mathematics 2022-12-12 Sachin S. Sharma , Priyanshu Chakraborty , Ritesh Kumar Pandey , S. Eswara Rao

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…

Representation Theory · Mathematics 2025-08-18 Sudipta Mukherjee

In the present paper, we prove that any finite non-trivial irreducible module over a rank two Lie conformal algebra $\mathcal{H}$ is of rank one. We also describe the actions of $\mathcal{H}$ on its finite irreducible modules explicitly.…

Representation Theory · Mathematics 2021-05-31 Maosen Xu , Yanyong Hong , Zhixiang Wu

In this paper, it is proved that all irreducible Harish-Chandra modules over the $\Q$ Heisenberg-Virasoro algebra are of intermediate series (all weight spaces are 1-dimensional).

Representation Theory · Mathematics 2010-03-19 Xiangqian Guo , Xuewen Liu , Kaiming Zhao

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…

Representation Theory · Mathematics 2025-12-11 Souvik Pal

We define the notion of {\it strongly interlocked} for indecomposable generalized modules for a vertex operator algebra, and show that the notion of graded pseudo-trace is well defined for modules which satisfy this property in certain…

Quantum Algebra · Mathematics 2026-03-09 Katrina Barron , Karina Batistelli , Florencia Orosz Hunziker , Gaywalee Yamskulna

We first define a class of non-weight modules over the N=1 Heisenberg-Virasoro superalgebra $\mathfrak{g}$, which are reducible modules. Then we give all submodules of such modules, and present the corresponding irreducible quotient modules…

Representation Theory · Mathematics 2025-08-13 Ziqi Hong , Haibo Chen , Yucai Su

We prove that an irreducible quasifinite module over the central extension of the Lie algebra of $N\times N$-matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate…

Representation Theory · Mathematics 2007-05-23 Yucai Su

In this paper, we study a class of non-weight modules over the affine-Virasoro algebra of type $A_1$, which are free modules of rank one when restricted to the Cartan subalgebra (modulo center). We give the classification of such modules.…

Representation Theory · Mathematics 2019-09-04 Qiufan Chen , Jianzhi Han