Geometric $R$ matrices and discrete integrable systems: a study for deriving differential equations (Combinatorial Representation Theory and Connections with Related Fields)

Abstract

We present two types of systems of differential equations that can be derived from a set of discrete integrable systems which is associated with the geometric R matrices. One is a kind of extended Lotka-Volterra systems, and the other seems to be generally new but reduces to a previously known system in a special case. Both equations are related to Lax equations associated with the loop elementary symmetric functions. It is a related work done after the talk at RIMS on 19 October 2021, and based on the preprint (arXiv:2203:12325). Interested readers can read the preprint for details and references.