Jim LepowskyAffiliation: Rutgers University Email: lepowsky@math.rutgers.edu Title Of Talk: ``Motivated proofs'' of generalized RogersRamanujan 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 RogersRamanujan 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 vertexoperatoralgebraic approaches to the RogersRamanujan identities and generalizations. I'll survey a number of recent developments on ''motivated proofs'' of families of partition identities of RogersRamanujan 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 longterm 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.
