# Affine lie algebras, vertex operator algebras and combinatorial identities

Abstract (Summary)

COOK, WILLIAM JEFFREY. Affine Lie Algebras, Vertex Operator Algebras and
Combinatorial Identities. (Under the direction of Kailash C. Misra and Haisheng Li)
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 ˜g is an untwisted affine Lie algebra and k is a positive
integer, the integrable highest weight ˜g-module L(k?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 ˜g. In the case when ˜g is of
(ADE)-type and k = 1, we solve the recurrence relations and obtain the full characters
of the adjoint module L(?0). Then, taking the principal specialization, we obtain new
families of multisum identities of Rogers-Ramanujan type.
Bibliographical Information:

Advisor:

School:North Carolina State University

School Location:USA - North Carolina

Source Type:Master's Thesis

Keywords:north carolina state university

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