Related papers: A class of simple weight Virasoro modules

We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two…

We generalize the modular invariance approach to include the half-integral weight modular forms. Accordingly the modular group should be extended to its metaplectic covering group for consistency. We introduce the well-defined half-integral…

In this paper, we complete the classification of the {\bf Z}-graded modules of the intermediate series over the $q$-analog Virasoro-like algebra $L$. We first construct four classes of irreducible {\bf Z}-graded $L$-modules of the…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

We classify simple weight modules with finite-dimensional weight spaces over the (centrally extended complex) Schr\"odinger algebra in (1+1)-dimensional space-time. Our arguments use the description of lowest weight modules by Dobrev,…

The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for $E_{8}$ or its highest weight is minuscule. In this paper, we prove…

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…

A regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient conditions under which a rational vertex…

Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$ having rank $l$ and let $V=L(\lambda)$ be an irreducible finite-dimensional $\mathfrak{g}$-module having highest weight $\lambda.$ Computations of weight multiplicities in…

For a simple Lie algebra $\mathfrak{g}$ of type $A_n,B_n,C_n$ or $D_n$, we give a characterization of the set of dominant integral weights $\lambda$ such that for any rational point $\mu$ in the fundamental Weyl chamber, $2\lambda-\mu$ is a…

In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1…

This paper is devoted to constructing simple modules of the planar Galilean conformal algebra. We study the tensor products of finitely many simple $\mathcal{U}(\mathcal{H})$-free modules with an arbitrary simple restricted module, where…

We study modules over a generalized Weyl algebra $R(\sigma,a)$ which are free when restricted to the base ring $R$. When $R$ is an integral domain, we construct all such finite-rank modules up to isomorphism, leading to new simple modules…

For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra $A$ of functions and the Lie algebra $\mathcal{V}$ of vector fields on the variety. We prove that a gauge…

We completely determine the minimal polynomial of an arbitrary simple highest weight module $L(\lambda)$ over a complex classical Lie algebra $\mathfrak{g}\subseteq\mathfrak{gl}_N$ relative to its defining module $\pi=\mathbb{C}^{N}$. These…

In this paper, we obtain a class of $\mathbb{Z}$-graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra. More precisely, we classify $\mathbb{Z}$-graded conformal algebras $\mathcal{A} =…

We say that a countable discrete group $\Gamma$ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every $\Gamma$- invariant von Neumann subalgebra $\mathcal{M}$ in $L(\Gamma)$ is of the form $L(\Lambda)$ for some…

In this note we show that the irreducible twisted modules of a holomorphic, $C_2$-cofinite vertex operator algebra $V$ have $L_0$-weights at least as large as the smallest $L_0$-weight of $V$. Hence, if $V$ is of CFT-type, then the twisted…

A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the subalgebra. From a finer viewpoint, a subalgebra is $\lambda$-wide if the simple module of a…

Let $V\subseteq A$ be a conformal inclusion of vertex operator algebras and let $\mathcal{C}$ be a category of grading-restricted generalized $V$-modules that admits the vertex algebraic braided tensor category structure of…