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Related papers: A class of simple weight Virasoro modules

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We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We…

Quantum Algebra · Mathematics 2014-01-23 Michael P. Tuite , Hoang Dinh Van

We describe the structure of the irreducible highest weight modules for the twisted Heisenberg-Virasoro Lie algebra at level zero. We prove that such a module is either isomorphic to a Verma module or to a quotient of two Verma modules.

Representation Theory · Mathematics 2012-11-06 Yuly Billig

In this paper we introduce and study $n$-point Virasoro algebras, $\tilde{\W_a}$, which are natural generalizations of the classical Virasoro algebra and have as quotients multipoint genus zero Krichever-Novikov type algebras. We determine…

Representation Theory · Mathematics 2013-09-02 Ben Cox , Xiangqian Guo , Rencai Lu , Kaiming Zhao

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 classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from…

Representation Theory · Mathematics 2012-10-22 Vyacheslav Futorny , Dimitar Grantcharov , Volodymyr Mazorchuk

Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…

Representation Theory · Mathematics 2007-10-20 S. Eswara Rao , Vyacheslav Futorny

We classify simple bounded weight modules over the complex simple Lie superalgebras $\mathfrak{sl}(\infty |\infty)$ and $\mathfrak{osp} (m | 2n)$, when at least one of $m$ and $n$ equals $\infty$. For $\mathfrak{osp} (m | 2n)$ such modules…

Representation Theory · Mathematics 2022-05-17 Dimitar Grantcharov , Ivan Penkov , Vera Serganova

In this paper, we construct and classify a class of non-weight modules over the BMS-Kac-Moody algebra, which are free modules of rank one when restricted to the universal enveloping algebra of the Cartan subalgebra (modulo center). We give…

Representation Theory · Mathematics 2025-07-04 Qiufan Chen , Cong Guo

In this paper we study general highest weight modules $\mathbb{V}^\lambda$ over a complex finite-dimensional semisimple Lie algebra $\mathfrak{g}$. We present three formulas for the set of weights of a large family of modules…

Representation Theory · Mathematics 2016-03-02 Apoorva Khare

Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…

Quantum Algebra · Mathematics 2007-12-22 Yi-Zhi Huang

All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.

Representation Theory · Mathematics 2009-10-06 Ivan Dimitrov , Dimitar Grantcharov

In this paper we classify all simple weight modules for a quantum group $U_q$ at a complex root of unity $q$ when the Lie algebra is not of type $G_2$. By a weight module we mean a finitely generated $U_q$-module which has finite…

Representation Theory · Mathematics 2015-07-24 Dennis Hasselstrøm Pedersen

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

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice…

q-alg · Mathematics 2009-10-30 C. Dong , R. L. Griess , G. Hoehn

We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of…

Quantum Algebra · Mathematics 2020-11-18 Xiaoli Kong , Hongjia Chen , Chengming Bai

A class of generalized Verma modules over sl(m+1) are constructed from simple highest weight gl(m)-modules. Furthermore, the simplicity criterion for these sl(m+1)-modules are determined and an equivalence between generalized Verma modules…

Representation Theory · Mathematics 2025-06-25 Yaohui Xue , Yan Wang

It is shown that there are no simple mixed modules over the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a nontrivial finite-dimensional weight space, is a Harish-Chandra…

Rings and Algebras · Mathematics 2017-03-16 Huanxia Fa , Jianzhi Han , Junbo Li

In this paper, we generalize a result by Berman and Billig on weight modules over Lie algebras with polynomial multiplication. More precisely, we show that a highest weight module with an exp-polynomial ``highest weight'' has finite…

Representation Theory · Mathematics 2007-05-23 Yuly Billig , Kaiming Zhao

In arXiv:1811.04649, we extended the Dong-Mason theorem on irreducibility of modules for cyclic orbifold vertex algebras to the entire category weak modules and applied this result to Whittaker modules. In this paper we present further…

Quantum Algebra · Mathematics 2024-09-04 Drazen Adamovic , Ching Hung Lam , Veronika Pedic Tomic , Nina Yu

We classify Jet modules for the Lie (super)algebras $\mathfrak{L}=W\ltimes(\mathfrak{g}\otimes\mathbb{C}[t,t^{-1}])$, where $W$ is the Witt algebra and $\mathfrak{g}$ is a Lie superalgebra with an even diagonlizable derivation. Then we give…

Representation Theory · Mathematics 2020-07-07 Yan-an Cai , Rencai Lü , Yan Wang