Representations of the Hecke Group G(2) from Fermionic Modular Categories

Abstract

This project explores a conjecture which states that groups from the Fermionic Modular Category are finite; specifically representations of the Hecke group G(2) will be explored which are important in number theory. These representations are used for a mathematical model of Topological Quantum Computation (TQC) based on topological symmetries rather than geometric symmetries. The use of topological symmetries reduces the effects of outside interference on computations due to the nature of topological symmetries relying on the general shape instead of particular distances or angles. TQC would aid in the development of quantum computing by helping to solve the problem of interference in quantum particles. Magma algebraic software was used in order to generate these group representations and provide information on their resulting structure to aid in identification.