Orateur
Rinat KEDEM
(University of Illinois Urbana-Champaign)
Description
Glick’s cluster algebra for the pentagram map can be considered as the $A_\infty$ T-system cluster algebra wrapped on a special torus. A closely related integrable system is obtained by considering the T-system on a cylinder of radius 2. Its quantization is the relativistic quantum Toda chain, whose Hamiltonians commute with the time evolution operator for this cluster algebra, a generalized mutation sequence. I will explain how a different cluster algebra quiver, representing the T-system relations, can be quantized and the cluster variables used to construct the eigenfunctions of the Toda Hamiltonians. [Joint with P. Di Francesco]