Related papers: Automorphisms and Verma modules for Generalized Sc…

In this paper, we study representations of the vertex operator algebra $L(k,0)$ at one-third admissible levels $k= -5/3, -4/3, -2/3$ for the affine algebra of type $G_2^{(1)}$. We first determine singular vectors and then obtain a…

Let $A$ be the ring of elements in an algebraic function field $K$ over $\mathbb{F}_q$ which are integral outside a fixed place $\infty$. In contrast to the classical modular group $SL_2(\mathbb{Z})$ and the Bianchi groups, the {\it…

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.

Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this extension…

It is shown that the support of an irreducible weight module over the Schr\"{o}dinger-Virasoro Lie algebra with an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module…

In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($\mathcal{D}$-modules), and reformulate the…

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

Let $\preceq$ be a compatible total order on the additive group $\mathbb{Z}^2$, and $L$ be the rank two Heisenberg-Virasoro algebra. For any $\mathbf{c}=(c_1,c_2,c_3,c_4) \in \mathbb{C}^4$, we define $\mathbb{Z}^2$-graded Verma module…

Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted…

For any nullity $2$ extended affine Lie algebra $\mathcal{E}$ of maximal type and $\ell\in\mathbb{C}$, we prove that there exist a vertex algebra $V_{\mathcal{E}}(\ell)$ and an automorphism group $G$ of $V_{\mathcal{E}}(\ell)$ equipped with…

Let $G\subset GL(V)$ be a linear Lie group with Lie algebra $\frak g$ and let $A(\frak g)^G$ be the subalgebra of $G$-invariant elements of the associative supercommutative algebra $A(\frak g)= S(\frak g^*)\otimes \La(V^*)$. To any…

In this paper we face the study of the representations of the exceptional Lie superalgebra E(5,10). We recall the construction of generalized Verma modules and give a combinatorial description of the restriction to sl_5 of the Verma module…

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$-isometry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V^G-modules which occur as submodules of irreducible V-modules by using intertwining operators for…

Motivated by the structure of certain modules over the loop Virasoro Lie conformal algebra and the Lie structures of Schrodinger-Virasoro algebras, we construct a class of infinite rank Lie conformal algebras CSV (a, b), where a, b are…

We classify the irreducible modules for the fixed point vertex operator subebra of the rank 1 free bosonic VOA under the -1 automorphism.

In this paper we construct resolutions of finite dimensional irreducible gl(m|n)-modules in terms of generalized Verma modules. The resolutions are determined by the Kostant cohomology groups and extend the strong…

In this paper, we classify all irreducible weight modules with finite-dimensional weight spaces over the affine-Virasoro Lie algebra of type $A_1$.

For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $\sigma$ that commutes with $d$, we introduce the $(d,\sigma)$-twisted Affine-Virasoro…

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.