Mini-Workshop: Three Facets of R-Matrices

Abstract

By definition, an R–matrix with spectral parameter is a solution to the Yang–Baxter equation, introduced in the 1970’s by C.N. Yang and R.J. Baxter. Such a matrix encodes the Boltzmann weights of a lattice model of statistical mechanics, and the Yang–Baxter equation appears naturally as a sufficient condition for its solvability.

In the last decade, several mathematical and physical theories have led to seemingly different constructions of R–matrices. The theme of this workshop was the interaction of three such approaches, each of which has independently proven to be valuable: the geometric, analytic and gauge–theoretic constructions of R-matrices. Its aim was to bring together leading experts and researchers from each school of thought, whose recent works have given novel interpretations to this nearly classical topic.