Related papers: On the concepts of intertwining operator and tenso…

We generalize the notion of an intertwining operator to N-graded weak modules over a vertex operator algebra and study their properties. We show a formula for the dimensions of these intertwining operators in terms of modules over the Zhu…

We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…

We discuss a recent proof by the author of a general version of the Verlinde conjecture in the framework of vertex operator algebras and the application of this result to the construction of modular tensor tensor category structure on the…

This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

Linear operators $R$ are introduced on tensor products of evaluation modules of $U'_q\bigl(\widehat{sl}(2)\bigr)$ obtained from the complementary and strange series representations. The operators $R$ satisfy the intertwining condition on…

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…

We define an integral intertwining operator among modules for a vertex operator algebra to be an intertwining operator which respects integral forms in the modules, and we show that an intertwining operator is integral if it is integral…

This is the second part in a series of papers presenting a theory of tensor products for module categories for a vertex operator algebra. In Part I (hep-th/9309076), the notions of $P(z)$- and $Q(z)$-tensor product of two modules for a…

Ternary algebras, constructed from ternary commutators, or as we call them, ternutators, defined as the alternating sum of products of three operators, have been shown to satisfy cubic identities as necessary conditions for their existence.…

We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable…

For a vertex operator algebra $V$, we construct an explicit isomorphism between the space of genus-0 conformal blocks associated to permutation-twisted $V^{\otimes n}$-modules and the space of conformal blocks associated to untwisted…

In the present paper we construct explicitly the intertwining differential operators for the Jacobi algebra ${\cal G}_2.$ For the construction we use the singular vectors of the Verma modules over ${\cal G}_2$ which we have constructed…

Let $V_1 \otimes V_2$ be a tensor product of VOAs. Using Zhu theory we discuss the theory of representations of V (associative algebra, modules and fusion rules). We prove that this theory is more or less the same as representation theory…

This is the third part of the revised versions of the notes of three consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi Huang in the conference on Monster and vertex operator algebras at the Research Institute…

It is well known that the Jacobi operators completely determine the curvature tensor. The question of existence of a curvature tensor for given Jacobi operators naturally arises, which is considered and solved in the previous work.…

We reformed the tensor product theory of vertex operator algebras developed by Huang and Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2-cofiniteness. We also showed that the tensor product theory develops…

We introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let $V$ be a vertex operator algebra and let $g_{1}$, $g_{2}$…

We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the…

In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving monodromies. The problem of constructing…

There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…