English
Related papers

Related papers: New simple modules for the $W$-algebra $W(2,2)$

200 papers

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…

Representation Theory · Mathematics 2025-06-05 Haibo Chen , Yucai Su , Yukun Xiao

We quantize the $W$-algebra W(2,2), whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.

Rings and Algebras · Mathematics 2008-02-04 Junbo Li , Yucai Su

In this paper, we give a construction of simple modules generalizing and including both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We…

Representation Theory · Mathematics 2019-06-21 Dong Liu , Yufeng Pei , Limeng Xia

We show that subsingular vectors exist in Verma modules over W(2,2), and present a subquotient structure of these modules. We prove conditions for irreducibility of a tensor product of intermediate series module with the highest weight…

Representation Theory · Mathematics 2013-08-12 Gordan Radobolja

We generalize a construction of Bell and Rogalski to realize new examples of $\mathbb{Z}^n$-graded simple rings. This construction also generalizes TGWAs of type $(A_1)^n$. In addition to considering basic properties of these algebras, we…

Rings and Algebras · Mathematics 2025-06-26 Jason Gaddis , Daniele Rosso , Robert Won

In an attempt to get some information on the multiplicative structure of the Green ring we study algebraic modules for simple groups, and associated groups such as quasisimple and almost-simple groups. We prove that, for almost all groups…

Representation Theory · Mathematics 2011-02-18 David A Craven

Let $W_n^+$ be the Lie algebra of the Lie algebra of vector fields on $\C^n$. In this paper, we classify all simple bounded weight $W_n^+$ modules. Any such module is isomorphic to the simple quotient of a tensor module $F(P,M)=P\otimes M$…

Representation Theory · Mathematics 2020-01-14 Yaohui Xue , Rencai Lü

In the present paper, a class of new simple modules over the $N=1$ Ramond algebra are constructed, which are induced from simple modules over some finite dimensional solvable Lie superalgebras. These new modules are simple restricted…

Quantum Algebra · Mathematics 2023-02-08 Haibo Chen

We introduce a tensor category O_+ (resp. O_{-}) of certain modules of gl_{\infty} with non-negative (resp. non-positive) integral central charges with the usual tensor product. We also introduce a tensor category O_f consisting of certain…

q-alg · Mathematics 2008-02-03 Weiqiang Wang

In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras $W_n$, we explicitly describe supports of such modules. We also obtain some descriptions on the…

Representation Theory · Mathematics 2009-06-05 Volodymyr Mazorchuk , Kaiming Zhao

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…

Representation Theory · Mathematics 2023-05-31 Dong Liu , Yufeng Pei , Limeng Xia

We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification…

Representation Theory · Mathematics 2007-05-23 Jonas T. Hartwig

Let $A_{m,n}$ be the tensor product of the Laurient polynomial algebra in $m$ even variables and the exterior algebra in $n$ odd variables over the complex field $\bC$, and the Witt superalgebra $W_{m,n}$ be the Lie superalgebra of…

Representation Theory · Mathematics 2020-01-14 Yaohui Xu , Rencai Lü

We construct a new family of simple $\mathfrak{gl}_{2n}$-modules which depends on $n^2$ generic parameters. Each such module is isomorphic to the regular $U(\mathfrak{gl}_{n})$-module when restricted the $\mathfrak{gl}_{n}$-subalgebra…

Representation Theory · Mathematics 2017-07-11 Jonathan Nilsson

In this paper, we classify all irreducible weight modules with finite dimensional weight spaces over the $W$-algebra $W(2, 2)$. Meanwhile, all indecomposable modules with one dimensional weight spaces over the $W$-algebra $W(2, 2)$ are also…

Representation Theory · Mathematics 2008-01-18 Dong Liu , Linsheng Zhu

This paper gives two results on the simple modules for the Brauer algebra over the complex field. First we describe the module structure of the restriction of all simple modules. Second we give a new geometrical interpretation of Ram and…

Representation Theory · Mathematics 2012-06-01 Maud De Visscher , Paul P. Martin

In this paper, we present a class of non-weight Virasoro modules $\mathcal{M}\big(V,\Omega(\lambda_0,\alpha_0)\big)\otimes\bigotimes_{i=1}^m\Omega(\lambda_i,\alpha_i)$ where $\Omega(\lambda_i,\alpha_i)$ and…

Representation Theory · Mathematics 2022-03-22 Haibo Chen , Jianzhi Han , Yanyong Hong , Yucai Su

Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of…

Quantum Algebra · Mathematics 2024-11-01 Gastón Andrés García , Cristian Vay

In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible…

Quantum Algebra · Mathematics 2007-11-30 W. Zhang , C. Dong

In this paper, we construct a class of simple weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras from restricted modules over some positive part subalgebra of the twisted Heisenberg-Virasoro algebra.…

Representation Theory · Mathematics 2026-03-09 Chengkang Xu , Fen Zhang