Related papers: The relationship between skew group algebras and o…
We investigate the general structure of the automorphism group and the Lie algebra of derivations of a finitely generated vertex operator algebra. The automorphism group is isomorphic to an algebraic group. Under natural assumptions, the…
An irreducible module for the parafermion vertex operator algebra $K(\mathfrak{sl}_2,k)$ is said to be of $\sigma$-type if an automorphism of the fusion algebra of $K(\mathfrak{sl}_2,k)$ of order $k$ is trivial on it. For any integer $k \ge…
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…
This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…
We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the…
We determine the graded composition multiplicity in the symmetric algebra S(V) of the natural GL_n(q)-module V, or equivalently in the coinvariant algebra of V, for a large class of irreducible modules around the Steinberg module. This was…
In this paper we study representations of skew group algebras $\Lambda G$, where $\Lambda$ is a connected, basic, finite-dimensional algebra (or a locally finite graded algebra) over an algebraically closed field $k$ with characteristic $p…
We introduce and study an affine analogue of skew Young diagrams and tableaux on them. It turns out that the double affine Hecke algebra of type $A$ acts on the space spanned by standard tableaux on each diagram. It is shown that the…
We give a general, direct and explicit construction of lower-bounded generalized twisted modules satisfying a universal property for a grading-restricted vertex (super)algebra $V$ associated to an automorphism $g$ of $V$. In particular,…
Let $X$ and $\mathfrak{a}$ be an affine scheme and (respectively) a finite-dimensional associative algebra over an algebraically-closed field $\Bbbk$, both equipped with actions by a linearly-reductive linear algebraic group $G$. We…
We study a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by $\mathbb{Z}_{2k}$. Based on those simple current modules, a vertex operator algebra associated with a…
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…
We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…
In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain…
Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V. We give two sufficient conditions implying that V is energy-bounded. The first condition is…
We study the meromorphic open-string vertex algebras and their modules over the two-dimensional Riemannian manifolds that are complete, connected, orientable, and of constant sectional curvature $K\neq 0$. Using the parallel tensors, we…
In vertex operator algebra theories, most of the general theorems are proved under the assumptions of rationality and C_2-cofiniteness. In this paper, we obtain several general theorems without the assumption of rationality so that we can…
This paper is about the orbifold theory of affine vertex operator superalgebras. Among the main results, we classify the irreducible modules and determine the fusion rules for the orbifold of the simple affine vertex operator superalgebra…
We construct a certain topological algebra $\Ext ^{\sharp}_{G ^{\vee}} X (\chi)$ from a Deligne-Langlands parameter space $X (\chi)$ attached to the group of rational points of a connected split reductive algebraic group $G$ over a…
A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible subgroups of exceptional algebraic groups $G$ which are connected, closed and…