Related papers: Classification of bounded modules for the Twisted …

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

We give a complete description of the full automorphism group of a lattice vertex operator algebra, determine the twisted Zhu's algebra for the automorphism lifted from the -1 isometry of the lattice and classify the corresponding…

We show that the representation theory for the toroidal extended affine Lie algebras is controlled by a vertex operator algebra which is a tensor product of four VOAs: a sub-VOA of the hyperbolic lattice VOA, two affine VOAs and a Virasoro…

Since 2020, finite weight modules have been studied over twisted affine Lie superalgebras. To complete the characterization of modules over affine Lie superalgebras, we need some information regarding modules over untwisted affine Lie…

We classify the simple quantum group modules with finite dimensional weight spaces when the quantum parameter $q$ is transcendental and the Lie algebra is not of type $G_2$. This is part $2$ of the story. The first part being Irreducible…

We classify integrable bounded simple weight modules over classical Lie superalgebras at infinity. We also study the categories of such modules, and we prove that for most of the classical Lie superalgebras at infinity the respective…

We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex…

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…

Let $\Lambda $ be an artin algebra and $T$ a $\tau$-tilting $\Lambda$-module. We prove that $T$ is a tilting module if and only if ${\rm Ext}_{\Lambda}^{i}(T,\Fac T)=0$ for all $i\geq 1$, where $\Fac T$ is the full subcategory consisting of…

Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several…

In this paper, we introduce a class of infinite Lie conformal algebras $\mathfrak{B}(\alpha,\beta,p)$, which are the semi-direct sums of Block type Lie conformal algebra $\mathfrak{B}(p)$ and its non-trivial conformal modules of $\Z$-graded…

A commutative associative algebra $A$ over ${\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an…

Twisted loop algebras of the second kind are infinite-dimensional Lie algebras that are constructed from a semisimple Lie algebra and an automorphism on it of order at most $2$. They are examples of equivariant map algebras. The…

We associate to an arbitrary positive root $\alpha$ of a complex semisimple finite-dimensional Lie algebra $\mfrak{g}$ a twisting endofunctor $T_\alpha$ of the category of $\mfrak{g}$-modules. We apply this functor to generalized Verma…

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

We continue with [LY] to construct and classify graded simple twisted modules for the $\N$-graded vertex algebras constructed by Gorbounov, Malikov and Schechtman from vertex algebroids. Meanwhile we determine the full automorphism groups…

Recently Terwilliger and the present author found a presentation for the three-point $\mathfrak{sl}_2$ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra $\boxtimes$ by generators and relations…

In this paper, we investigate the theory of $g$-twisted modules for modular $\frac{1}{2}\mathbb{Z}$-graded vertex superalgebras over an algebraically closed field $\mathbb{F}$ of prime characteristic $p>2$. For a…

In 2006, Gao and Zeng \cite{GZ} gave the free field realizations of highest weight modules over a class of extended affine Lie algebras. In the present paper, applying the technique of localization to those free field realizations, we…

We present complete realization of irreducible $A_1 ^{(1)}$-modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal…