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## "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.