We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

Modularity and tensor categories for affine vertex algebras at admissible level

Formal Metadata

Title
Modularity and tensor categories for affine vertex algebras at admissible level
Title of Series
Number of Parts
9
Author
License
CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
A well-known result is that modules of a rational vertex algebra form a modular tensor category and that the modular group action on graded traces coincides with the categorical one. Prime examples are affine vertex algebras at positive integer level. I would like to explain the state of the art for affine vertex algebras at admissible level and our knowledge is mainly restricted to the case of sl(2). From the character point of view three types of traces arise: vector-valued modular forms, meromorphic Jacobi forms and formal distributions. There are also three types of categories one can associate to the affine vertex algebra and categorical action of the modular group seems to coincide with the one on characters.