home | literature reviews

"Congruence subgroups and generalized Frobenius-Schur indicators", Siu-Hung Ng, Peter Schauenburg, 2010

Reviewed August 25, 2023

Citation: Ng, Siu-Hung, and Peter Schauenburg. "Congruence subgroups and generalized Frobenius-Schur indicators." Communications in Mathematical Physics 300.1 (2010): 1-46.

Web: https://arxiv.org/abs/0806.2493

Tags: Mathematical, Modular-tensor-categories, Foundational

This paper proves that the kernel of the modular representation of every modular tensor category is a congruence subgroup of SL2(Z). That is, it contains the subgroup of matrices congruent to the identity modulo N, for some fixed integer N.

To prove this theorem, they introduce a generalized Frobenius-Schur inducator. These indicators have since found uses in other papers as well.