Related papers: The irreducible modules and fusion rules for the p…
The rationality of the parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra and any nonnegative integer is established and the irreducible modules are determined.
The quantum dimensions and the fusion rules for the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k are determined.
Fusion rules among irreducible modules of the free bosonic orbifold vertex operator algebra are completely determined.
In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…
Irreducible modules of the 3-permutation orbifold of a rank one lattice vertex operator algebra are listed explicitly. Fusion rules are determined by using the quantum dimensions. The $S$-matrix is also given.
This paper is about the orbifold theory of affine and parafermion vertex operator algebras. It is known that the parafermion vertex operator algebra $K(sl_2,k)$ associated to the integrable highest weight modules for the affine Kac-Moody…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k coincides with a certain W-algebra. In particular, a set of generators for…
We discuss some applications of fusion rules and intertwining operators in the representation theory of cyclic orbifolds of the triplet vertex operator algebra. We prove that the classification of irreducible modules for the orbifold vertex…
The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
The trace functions for the Parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra $\g$ and any positive integer $k$ are studied and an explicit modular transformation formula of the trace functions is…
We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras $A_{k}(sl(2))$ for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible modules are…
It is proved that the regularity of parafermion vertex operator algebras associated to integrable highest weight modules for affine Kac-Moody algebra A_1^{(1)} implies the C_2-cofiniteness of parafermion vertex operator algebras associated…
Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V^G-modules which occur as submodules of irreducible V-modules by using intertwining operators for…
We construct new irreducible weight modules over quantum affine algebras of type I with all weight spaces infinite-dimensional. These modules are obtained by parabolic induction from irreducible modules over the Heisenberg subalgebra.
The parafermionic cosets $C_k = \mathrm{Com} (H, L_k(\mathfrak{sl}_2) )$ are studied for negative admissible levels $k$, as are certain infinite-order simple current extensions $B_k$ of $C_k$. Under the assumption that the tensor theory…
In this paper, the irreducible modules for the $\mathbb{Z}_{2}$-orbifold vertex operator subalgebra of the parafermion vertex operator algebra associated to the irreducible highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$…
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…
We determine fusion rules (dimensions of the space of intertwining operators) among simple modules for the vertex operator algebra obtained as an even part of the symplectic fermionic vertex operator superalgebra. By using these fusion…