Date of Award

1-1-2011

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (iii, 72 pages)

Dissertation/Thesis Chair

Antun Milas

Committee Members

Christian Lenart, Alexandre Tchernev

Keywords

Vertex Algebras, Lattice theory, Vertex operator algebras

Subject Categories

Physical Sciences and Mathematics

Abstract

We explore the structure of a certain ``principal'' subalgebra, $W_L(\mathcal{B})$, of a lattice vertex (super)-algebra, $V_L$, where $L$ is a non-degenerate integral lattice, and $\mathcal{B}$ is a $\mathbb{Z}$-basis of $L$. Under a certain positivity condition on $\mathcal{B}$ we find a presentation of $W_L(\mathcal{B})$ and of $W_L(\mathcal{B})$-modules. In a more general case we also find their combinatorial bases. For both cases we calculate the (multi)-graded dimensions of modules expressed as fermionic $q$-series . This work generalizes some of the results from \cite{CalLM}, which involved a root lattice of type $A-D-E$, and where $\mathcal{B}$ was the set of simple roots.

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