English
Related papers

Related papers: Whittaker modules for the Schr\"odinger-Virasoro a…

200 papers

In this paper, we determine all simple restricted modules over the mirror Heisenberg-Virasoro algebra ${\mathfrak{D}}$, and the twisted Heisenberg-Virasoro algebra $\bar\mathfrak{D}$ with nonzero level. As applications, we characterize…

Representation Theory · Mathematics 2021-12-01 Haijun Tan , Yufeng Yao , Kaiming Zhao

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…

Rings and Algebras · Mathematics 2009-11-13 Junbo Li , Yucai Su

We consider the Whittaker modules $M_{1}(\lambda,\mu)$ for the Weyl vertex algebra $M$, constructed in arXiv:1811.04649, where it was proved that these modules are irreducible for each finite cyclic orbifold $M^{\Bbb Z_n}$. In this paper,…

Quantum Algebra · Mathematics 2021-12-17 Drazen Adamovic , Veronika Pedic Tomic

We extend the Dong-Mason theorem on the irreducibility of modules for orbifold vertex algebras from [C. Dong, G. Mason, Duke Math. J. 86 (1997)] 305-321] for the category of weak modules. Let $V$ be a vertex operator algebra, $g$ an…

Quantum Algebra · Mathematics 2022-01-14 Drazen Adamovic , Ching Hung Lam , Veronika Pedic Tomic , Nina Yu

In this paper we discuss the structure of the tensor product V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series and irreducible highest weight module over the Virasoro algebra. We generalize Zhang's…

Representation Theory · Mathematics 2013-08-12 Gordan Radobolja

This article is concerned with an extensive study of an infinite-dimensional Lie algebra $\mathfrak{sv}$, introduced in the context of non-equilibrium statistical physics, containing as subalgebras both the Lie algebra of invariance of the…

Mathematical Physics · Physics 2007-05-23 Claude Roger , Jeremie Unterberger

In this paper, the property and the classification the simple Whittaker modules for the schr\"{o}dinger algebra are studied. A quasi-central element plays an important role in the study of Whittaker modules of level zero. For the Whittaker…

Representation Theory · Mathematics 2013-11-12 Xiufu Zhang , Yongsheng Cheng

We use Block's results to classify irreducible modules over the differential operator algebra $\mathbb{C}[t,t^{-1}, \frac d{dt}]$. From this classification and using "the twisting technique" we construct a lot of new irreducible modules…

Representation Theory · Mathematics 2019-08-09 Rencai Lu , Kaiming Zhao

We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Mili\v{c}i\'c-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra…

Representation Theory · Mathematics 2021-08-18 Chih-Whi Chen

In this paper, we introduce a finite Lie conformal superalgebra called the Heisenberg-Virasoro Lie conformal superalgebra $\mathfrak{s}$ by using a class of Heisenberg-Virasoro Lie conformal modules. The super Heisenberg-Virasoro algebra of…

Representation Theory · Mathematics 2023-05-30 Haibo Chen , Xiansheng Dai , Yanyong Hong

In this paper, we study Whittaker modules for a Lie algebras of Block type. We define Whittaker modules and under some conditions, obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules over this…

Representation Theory · Mathematics 2009-07-09 Bin Wang , Xinyun Zhu

We study various categories of Whittaker modules over the queer Lie superalgebras $\mathfrak q(n)$. We formulate standard Whittaker modules and reduce the problem of composition factors of these standard Whittaker modules to that of Verma…

Representation Theory · Mathematics 2026-01-01 Chih-Whi Chen , Shun-Jen Cheng

In this paper, we study Whittaker modules for graded Lie algebras. We define Whittaker modules for a class of graded Lie algebras and obtain a bijective correspondence between the set of isomorphism classes of Whittaker modules and the set…

Representation Theory · Mathematics 2009-03-04 Bin Wang

For any positive integer $n$, let $A_n=\mathbb{C}[t_1,\dots,t_n]$, $W_n=\text{Der}(A_n)$ and $\Delta_n=\text{Span}\{\frac{\partial}{\partial{t_1}},\dots,\frac{\partial}{\partial{t_n}}\}$. Then $(W_n, \Delta_n)$ is a Whittaker pair. A…

Representation Theory · Mathematics 2022-05-12 Yufang Zhao , Genqiang Liu

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…

Mathematical Physics · Physics 2024-03-07 Gaëtan Borot , Vincent Bouchard , Nitin Kumar Chidambaram , Thomas Creutzig

In this paper, a general setting is proposed to define a class of modules over nonsemisimple Lie algebras $\mathfrak{g}$ induced by a nonperfect ideal $\mathfrak{p}$. This class of Lie algebras includes many well-known Lie algebras, and…

Representation Theory · Mathematics 2025-08-11 Cunguang Cheng , Wenting Gao , Shiyuan Liu , Kaiming Zhao , Yueqiang Zhao

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

In this paper, Whittaker modules for the W-algebra W(2,2) are studied. We obtain analogues to several results from the classical setting and the case of the Virasoro algebra, including a classification of simple Whittaker modules by central…

Representation Theory · Mathematics 2009-02-23 Bin wang , Junbo Li

In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on…

Representation Theory · Mathematics 2024-03-20 Haibo Chen , Xiansheng Dai , Dong Liu , Yufeng Pei

In this paper, we obtain a class of irreducible Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega(\lambda,b)$ defined in [LZ], with irreducible highest weight modules $V(\theta,h)$ or with irreducible…

Representation Theory · Mathematics 2019-08-09 Haijun Tan , Kaiming Zhao