BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar Reconstruction of modular data from representations of SL(2,Z)
Reconstruction of modular data from representations of SL(2,Z)
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sébastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
Siu-Hung Ng
Time
Wednesday, June 15, 2022 10:30 AM - 11:30 AM
Venue
1110
Online
Zoom 361 038 6975 (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.