# Affine Lie Algebras, Vertex Operator Algebras and Combinatorial Identities

Abstract (Summary)

Affine Lie algebra representations have many connections with different areas of
mathematics and physics. One such connection in mathematics is with number theory
and in particular combinatorial identities. In this thesis, we study affine Lie
algebra representation theory and obtain new families of combinatorial identities
of Rogers-Ramanujan type.
It is well known that when $ ilde{g}$ is an untwisted affine Lie algebra and $k$ is a
positive integer, the integrable highest weight $ ilde{g}$-module $L(k Lambda_0)$
has the structure of a vertex operator algebra. Using this structure, we will obtain
recurrence relations for the characters of all integrable highest-weight modules of $ ilde{g}$.
In the case when $ ilde{g}$ is of (ADE)-type and k=1, we solve the recurrence relations
and obtain the full characters of the adjoint module $L(Lambda_0)$. Then, taking the principal
specialization, we obtain new families of multisum identities of Rogers-Ramanujan type.
Bibliographical Information:

Advisor:Haisheng Li; Bojko Bakalov; Jon Doyle; Kailash C. Misra

School:North Carolina State University

School Location:USA - North Carolina

Source Type:Master's Thesis

Keywords:mathematics

ISBN:

Date of Publication:03/24/2005