The non-semisimple Verlinde formula and pseudo-trace functions
Quantum Algebra
2019-10-24 v2 High Energy Physics - Theory
Category Theory
Abstract
We point out that results of Shimizu on internal characters imply a useful non-semisimple variant of the categorical Verlinde formula for factorisable finite tensor categories. When combined with results on pseudo-trace functions by Miyamoto and Arike-Nagatomo, one can make a precise conjecture for a non-semisimple modular Verlinde formula which relates modular properties of pseudo-trace functions and the product in the Grothendieck ring of the corresponding vertex operator algebra.
Cite
@article{arxiv.1605.04448,
title = {The non-semisimple Verlinde formula and pseudo-trace functions},
author = {A. M. Gainutdinov and I. Runkel},
journal= {arXiv preprint arXiv:1605.04448},
year = {2019}
}
Comments
37 pages