Publications (40)
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…
Vertex operator algebras and operads
Yi-Zhi Huang, James Lepowsky
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, th…
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-…
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, 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…
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…