Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
We address the open question of which representations of the modular group SL(2,Z) can be realized by a modular category. In order to investigate this problem, we introduce the concept of a symmetrizable representation of SL(2,Z) and show that this property is necessary for the representation to be realized. We then prove that all congruence representations of SL(2,Z) are symmetrizable. The proof involves constructing a symmetric basis, which greatly aids in further calculation. We apply this result to the reconstruction of modular category data from representations, as well as to the classification of semiregular categories, which are defined via an action of the Galois group Gal(Qbar/Q) on their simple objects.
Date
4-3-2023
Recommended Citation
Wilson, Samuel Nathan, "SL(2,Z) Representations and 2-Semiregular Modular Categories" (2023). LSU Doctoral Dissertations. 6094.
https://repository.lsu.edu/gradschool_dissertations/6094
Committee Chair
Ng, Siu-Hung
DOI
10.31390/gradschool_dissertations.6094