For a finite-dimensional simple Lie algebra gg, we use the vertex tensor category theory of
Huang and Lepowsky to identify the category of standard modules for the affine Lie algebra …

We study the representation theory of the Kazama–Suzuki coset vertex operator
superalgebra associated to the pair of a complex simple Lie algebra and its Cartan …

We study the structure of fusion rules for the triplet $ W $-algebra $\mathcal {W} _ {p_+, p_-}
$. By using the vertex tensor category theory developed by Huang, Lepowsky and Zhang …

We prove that certain screening operators in conformal field theory obey the algebra
relations of a corresponding Nichols algebra with diagonal braiding. Our result proves in …

Let V be the even part of the vertex operator super-algebra of r pairs of symplectic fermions.
Up to two conjectures, we show that V admits a unique holomorphic extension if r is a …

We show that Kazhdan and Lusztig's category $ KL^ k (\mathfrak {sl} _2) $ of modules for the
affine Lie algebra $\widehat {\mathfrak {sl}} _2 $ at an admissible level $ k $, equivalently …

In the braided context, we rederive a popular nonsemisimple fusion algebra from a Nichols
algebra. Together with the decomposition that we find for the product of simple Yetter …

Let F 25 F_25 be the family of irreducible lowest weight modules for the Virasoro algebra of
central charge 25 which are not isomorphic to Verma modules. Let L (25, 0) be the Virasoro …

Abstract The Monster Lie algebra m is a quotient of the physical space of the vertex algebra
V= V♮⊗ V 1, 1, where V♮ is the Moonshine module vertex operator algebra of Frenkel …

Two chiral aspects of the WZW model in an operator formalism are investigated. First, the
meaning of duality, or conjugation, of primary fields is clarified. On a class of modules …