Related papers: Irreducible tensor product modules over the affine…
For a twisted affine Lie superalgebra with nonzero odd part, we study {tight irreducible weight modules} with bounded weight multiplicities and show that if the action of nonzero real vectors of each affine component of the zero part is…
We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir \otimes A, where Vir is the Virasoro algebra and A is a Noetherian commutative associative unital algebra over the complex numbers. It is…
It is obtained that an irreducible weight module with finite weight multiplicities over a higher rank Virasoro or super-Virasoro algebra is either a module of the intermediate series, or a so-called finitely-dense module.
This work provides the first step toward the classification of irreducible finite weight modules over twisted affine Lie superalgebras. We study all such modules whether the canonical central element acts as a nonzero multiple of the…
Let $\mathcal{B}_r$ be the $(r+1)$-dimensional quotient Lie algebra of the positive part of the Virasoro algebra $\mathcal{V}$. Irreducible $\mathcal{B}_r$-modules were used to construct irreducible Whittaker modules in [MZ2] and…
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…
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…
We present the list of irreducible (generalized) highest weight modules over the Virasoro algebra and N=1 super-Virasoro algebras obtained as factor-modules of (generalized) Verma modules. We present also the character formulae of all these…
In this paper we study irreducible tensor products of representations of alternating groups in characteristics 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify…
We introduce a category B of bounded modules for the toroidal Lie algebras and study irreducible modules in B. We show that one of the irreducible modules in this category, L(T_0), admits a structure of a vertex operator algebra. We prove…
We study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie algebras. We construct new families of such…
In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We…
In this paper we classify the irreducible integrable modules for the loop affine-Virasoro algebra $(( \overset{\circ}{\mathfrak{g}} \otimes \mathbb{C}[t, t^{-1}] \oplus \mathbb{C} K) \rtimes \text{Vir}) \otimes A$, where $A$ is a finitely…
We study the properties of level zero modules over quantized affine algebras. The proof of the conjecture on the cyclicity of tensor products by Akasaka and the present author is given. Several properties of modules generated by extremal…
We study Demazure modules which occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie…
Let $n>1$ be an integer, $\alpha\in{\mathbb C}^n$, $b\in{\mathbb C}$, and $V$ a $\mathfrak{gl}_n$-module. We define a class of weight modules $F^\alpha_{b}(V)$ over $\sl_{n+1}$ using the restriction of modules of tensor fields over the Lie…
We classify integrable irreducible $\hat{g}[\sigma]$-modules in categories E and C, where E is proved to contain the well known evaluation modules and C to unify highest weight modules, evaluation modules and their tensor product modules.
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…
Toroidal Lie algebras are universal central extentions of the finite dimensional simple Lie algbera tensored with Laurent Polynomials in several commuteing variables. In this paper we classify irreducible integrable modules for Toroidal Lie…
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.