Jim Lepowsky

Affiliation: Rutgers University

Email: lepowsky@math.rutgers.edu

Title Of Talk: ``Motivated proofs'' of generalized Rogers-Ramanujan identities as stimuli for new ideas in vertex operator algebra theory

Abstract: Some years ago, G. Andrews and R. Baxter gave what they termed a ''motivated proof'' of the Rogers-Ramanujan identities. This proof, indeed ''motivated,'' on the one hand was in fact a variant of certain proofs of Rogers and Ramanujan, and on the other hand seemed to me to suggest new hidden structure in the ongoing vertex-operator-algebraic approaches to the Rogers-Ramanujan identities and generalizations. I'll survey a number of recent developments on ''motivated proofs'' of families of partition identities of Rogers-Ramanujan type, including work of B. Coulson, S. Kanade, R. McRae, F. Qi, M. Russell, S. Sadowski, A. Sills, C. Takita, M. Zhu and myself. Such proofs are expected to play an important role in the long-term interaction between the representation theory of vertex operator algebras and the theory of partitions. Recently, a new ''conceptual'' approach to such ''motivated proofs'' is being developed by my student Bud Coulson. I'll sketch these ideas.

Last update made Tue Feb 16 06:24:35 PST 2016.
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