[BIMSA-Tsinghua Quantum Symmetry Seminar] Reconstruction of modular data from representations of SL(2,Z)

 

Speaker:  Siu-Hung Ng

Time:     10:30-11:30

Date:       2022/06/15

Venue:     1129B

Zoom:361 038 6975     Passcode:BIMSA

 

Abstract: 

Modular data is the most important invariant of a modular tensor category. Associated to a modular data is a family of projectively equivalent linear representations of SL(2,Z), which are symmetric and congruence. One would naturally ask whether the representation type of these representations of SL(2,Z) could determine the underlying modular data. In fact, we have shown that for any congruence SL(2,Z) representation of dimension 6, it is either not realizable, or realized by a Galois conjugate of the modular data of a Deligne product of some quantum group modular tensor categories. This reconstruction process can be implemented for computer automation for higher dimensional congruence representations. This talk is based on joint work with Eric Rowell, Zhenghan Wang and Xiao-Gang Wen.