115 citations · 764 across the 40 of their papers we have counts for
27 papers · 1 filter
Braided tensor categories and extensions of vertex operator algebras
Yi-Zhi Huang, Alexander Kirillov, James Lepowsky
Let be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a…
Vertex-algebraic structure of principal subspaces of standard A_2^{(2)}-modules, I
Corina Calinescu, James Lepowsky, Antun Milas
Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affi…
Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) alg…
Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the seventh part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) al…
Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the sixth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) alge…
Logarithmic tensor category theory, V: Convergence condition for intertwining maps and the corresponding compatibility condition
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the fifth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) alge…
Logarithmic tensor category theory, IV: Constructions of tensor product bifunctors and the compatibility conditions
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the fourth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) alg…
Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) alge…
Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) alg…
Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules
Yi-Zhi Huang, James Lepowsky, Lin Zhang
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) alge…
Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E
Corina Calinescu, James Lepowsky, Antun Milas
Generalizing some of our earlier work, we prove natural presentations of the principal subspaces of the level one standard modules for the untwisted affine Lie algebras of types A,…
Logarithmic tensor product theory for generalized modules for a conformal vertex algebra
Yi-Zhi Huang, James Lepowsky, Lin Zhang
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories…
Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, II: higher level case
Corina Calinescu, James Lepowsky, Antun Milas
We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard A_1^(1)-modules. These pres…
Some developments in vertex operator algebra theory, old and new
James Lepowsky
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case
Corina Calinescu, James Lepowsky, Antun Milas
This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted a…
Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I
Yi-Zhi Huang, James Lepowsky, Lin Zhang
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories…
An equivalence of two constructions of permutation-twisted modules for lattice vertex operator algebras
Katrina Barron, Yi-Zhi Huang, James Lepowsky
The problem of constructing twisted modules for a vertex operator algebra and an automorphism has been solved in particular in two contexts. One of these two constructions is that…
From the representation theory of vertex operator algebras to modular tensor categories in conformal field theory
James Lepowsky
This is an expository article invited for the ``Commentary'' section of PNAS in connection with Y.-Z. Huang's article, ``Vertex operator algebras, the Verlinde conjecture, and modu…
On the concepts of intertwining operator and tensor product module in vertex operator algebra theory
Yi-Zhi Huang, James Lepowsky, Haisheng Li +1
We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general…
A logarithmic generalization of tensor product theory for modules for a vertex operator algebra
Yi-Zhi Huang, James Lepowsky, Lin Zhang
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generaliza…
Twisted vertex operators and Bernoulli polynomials
Benjamin Doyon, James Lepowsky, Antun Milas
Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie alge…
The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators
Stefano Capparelli, James Lepowsky, Antun Milas
Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for $\hat{\…
Twisted modules for vertex operator algebras and Bernoulli polynomials
Benjamin Doyon, James Lepowsky, Antun Milas
Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie alge…
The Rogers--Ramanujan recursion and intertwining operators
Stefano Capparelli, James Lepowsky, Antun Milas
We use vertex operator algebras and intertwining operators to study certain substructures of standard --modules, allowing us to conceptually obtain the classical Rogers-…