相关论文: McKay's observation and vertex operator algebras g…
In this paper we mainly study the vertex operator algebra $\mathbb{C} \mathrm{VA}(e, f)$ generated by two Ising vectors $e$ and $f$ with $\langle e, f\rangle=\frac{5}{2^{10}}$. We prove $\mathbb{C} \mathrm{VA}(e, f)$ is isomorphic to the…
We obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. Each braided VOA is…
Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They…
The observation that $n$ pairs of para-Bose (pB) operators generate the universal enveloping algebra of the orthosymplectic Lie superalgebra $osp(1/2n)$ is used in order to define deformed pB operators. It is shown that these operators are…
For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice…
Let $M^3 \subset \mathbb{C}^2$ be a $\mathcal{C}^\omega$ Levi nondegenerate hypersurface. In the literature, Cartan-Moser chains are detected from rather advanced considerations: either from the construction of a Cartan connection…
We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type $J$ on a punctured sphere. We denote the AD theories as $(J^b[k],Y)$, where $J^b[k]$ and…
One-point theta functions for modules of vertex operator algebras (VOAs) are defined and studied. These functions are a generalization of the character theta functions studied by Miyamoto and are deviations of the classical one-point…
We consider the semisimple orbits of a Vinberg $\theta$-representation. First we take the complex numbers as base field. By a case by case analysis we show a technical result stating the equality of two sets of hyperplanes, one…
In this paper, we introduce and study new classes of sub-vertex operator algebras of the lattice vertex operator algebras (VOAs), which we call the conic, Borel, and parabolic-type subVOAs. These CFT-type VOAs, which are not necessarily…
Permutation group algebras, and their generalizations called permutation centralizer algebras (PCAs), play a central role as hidden symmetries in the combinatorics of large $N$ gauge theories and matrix models with manifest continuous gauge…
We discuss a class of vertex operator algebras $\mathcal{W}_{m|n\times \infty}$ generated by a super-matrix of fields for each integral spin $1,2,3,\dots$. The algebras admit a large family of truncations that are in correspondence with…
We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are {\em simple currents} associated with semisimple weight one primary vectors. In the case that the…
In this paper we review the coset construction for winding subalgebras of affine Lie algebras. We classify all cosets of central charge $\hat c<1$ and calculate their branching rules. The corresponding character identities give certain…
We study global subalgebras of superconformal algebras in two dimensions and their unitary representations. Global superconformal multiplets are decomposed into conformal multiplets using Racah-Speiser algorithm, revealing many essential…
The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT's) and vertex operator algebras (VOA's). This cohomology theory produces…
We classify all non-invertible Kramers-Wannier duality defects in the $E_8$ lattice Vertex Operator Algebra (i.e. the chiral $(E_8)_1$ WZW model) coming from $\mathbb{Z}_m$ symmetries. We illustrate how these defects are systematically…
Borcherds-Kac-Moody algebras generalise finite-dimensional, simple Lie algebras. Scheithauer showed that there are exactly ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of…
We extend previous work by constructing a universal abelian tensor category ${\bf T}_t$ generated by two objects $X,Y$ equipped with finite filtrations $0\subsetneq X_0\subsetneq ... X_{t+1}\subsetneq X$ and $0\subsetneq Y_0\subsetneq ...…
The algebra generated by the down and up operators on a differential partially ordered set (poset) encodes essential enumerative and structural properties of the poset. Motivated by the algebras generated by the down and up operators on…