In this thesis, we study the VOA V_J,r associated to a Hermitian type Jordan algebra J, and mainly discuss the case when J is of B type. The content of this thesis is divided into three parts. The first part consists of Chapter 1, Chapter 2, and Chapter 3. We give a brief account of the theory of vertex algebra. We also review the VOAs V̄_J,1, V_J,r, where J is a B type Jordan algebra. The second part is from Chapter 4 to Chapter 6. We discuss some further properties of the VOA V_{J ,r}, where J is a B type Jordan algebra. We compute the correlation function of the fields associated to V_J,r, and give explicit constructions of the simple quotients V̄_J,r when r ∈ Z_≠0, using dual pair type constructions. We also calculate the character formula for the simple quotients V̄_J,r, r = -2n, n ≥ 1. The...[ Read more ]

In this thesis, we study the VOA V_J,r associated to a Hermitian type Jordan algebra J, and mainly discuss the case when J is of B type. The content of this thesis is divided into three parts. The first part consists of Chapter 1, Chapter 2, and Chapter 3. We give a brief account of the theory of vertex algebra. We also review the VOAs V̄_J,1, V_J,r, where J is a B type Jordan algebra. The second part is from Chapter 4 to Chapter 6. We discuss some further properties of the VOA V_{J ,r}, where J is a B type Jordan algebra. We compute the correlation function of the fields associated to V_J,r, and give explicit constructions of the simple quotients V̄_J,r when r ∈ Z_≠0, using dual pair type constructions. We also calculate the character formula for the simple quotients V̄_J,r, r = -2n, n ≥ 1. The third part is Chapter 7. We sketch the constructions of V_J,r for all Hermitian type Jordan algebras J. We also propose some problems for future study.