A note on quantum groups and integrable systems

Free-field formalism for quantum groups (preprint ITEP-M3/94, CRM-2202 hep-th/9409093) provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system (arXiv:1207.1869) is especially simple. This choice also fits into general framework of cluster varieties (math.AG/0311245) – natural changes of coordinates are cluster mutations.