Date of Award

2011

Degree Type

Thesis

Degree Name

M.A.Sc.

Department

Mathematics and Statistics

First Advisor

Yee, Wai (Economics, Mathematics, and Statistics)

Keywords

Mathematics.

Rights

CC BY-NC-ND 4.0

Abstract

The Virasoro algebra (\emph{Vir}) has important applications to the study of infinite dimensional Lie algebras, and specifically to areas of theoretical physics modeled by conformal field theories. The positive-energy representations of \emph{Vir} play a key role in string theory. A vital piece of information is the signature of the positive-energy representations. The physicist Adrian Kent calculated the characters of the signatures of these positive-energy representations in his paper. In this thesis, we will provide mathematical proofs for Kent's signature formulas for all possible values of the central charge and lowest weight. Furthermore, we simplify Kent's formulas by adopting a different approach to viewing the formulas. An important consequence is a clean reformulation in the minimal model case, which is of tremendous interest to theoretical physicists who wish to understand the modular group action in order to apply Kent's formulas to the study of non-unitary conformal field theories. We discuss how to compute the modular group action.

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