Q-systems: Discrete Integrability and Cluster Algebras

By Rinat Kedem

Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL

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Abstract

I’ll introduce a family of remarkable recursion relations, originally found in the context of the Bethe ansatz of generalized Heisenberg modules and quantum groups. I will reconsider this system as a discrete integrable system in its own right, and show some of the remarkable properties it and its quantization, via a cluster algebra formulation, exhibit. This will be a basic talk with no prior knowledge of any of the above mentioned topics assumed, with the purpose of introducing some of these structures and showing why they might be useful in mathematical physics.

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Researchers should cite this work as follows:

  • Rinat Kedem (2018), "Q-systems: Discrete Integrability and Cluster Algebras," http://nanohub.org/resources/28507.

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Location

REC 317, Purdue University, West Lafayette, IN