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Type of Document Dissertation Author Cook, William Jeffrey, Author's Email Address wjcook@ncsu.edu URN etd-03232005-234709 Title Affine Lie Algebras, Vertex Operator Algebras and Combinatorial Identities Degree PhD Graduate Program Mathematics Advisory Committee
Advisor Name Title Kailash C. Misra Committee Chair Haisheng Li Committee Co-Chair Bojko Bakalov Committee Member Jon Doyle Committee Member Keywords
- rogers-ramanujan combinartorial identities
- affine lie algebras
- vertex operator algebras
Date of Defense 2005-03-18 Availability unrestricted Abstract Affine Lie algebra representations have many connections with different areas ofmathematics 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.
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