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arXiv · 1605.04448

The non-semisimple Verlinde formula and pseudo-trace functions

A. M. Gainutdinov·I. Runkel
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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.

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A. M. Gainutdinov, I. Runkel. 2016-05-14. The non-semisimple Verlinde formula and pseudo-trace functions. https://arxiv.org/abs/1605.04448

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