Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups

TL;DR

This paper derives formulas for global dimensions of fusion categories from Lie groups at level k and their conformal embeddings, expressed through Lie quantum superfactorials, linking to special functions like the quantum Barnes function.

Contribution

It provides explicit formulas for global dimensions of fusion categories associated with Lie groups and conformal embeddings, using Lie quantum superfactorials.

Findings

Formulas for global dimensions in terms of Lie quantum superfactorials

Connection between superfactorials and the quantum Barnes function for type Ar

Application to conformal embeddings in fusion categories

Abstract

We obtain formulae giving global dimensions for fusion categories defined by Lie groups G at level k and for the associated module-categories obtained via conformal embeddings. The results can be expressed in terms of Lie quantum superfactorials of type G. The later are related, for the type Ar, to the quantum Barnes function.