Invariance of polymer partition functions under the geometric RSK correspondence

Understand

We prove that the values of discrete directed polymer partition functions involving multiple non-intersecting paths remain invariant under replacing the background weights by their images under the geometric RSK correspondence.

• This result is inspired by a recent and remarkable identity proved by Dauvergne, Orthmann and Vir\'ag which is recovered as the zero-temperature, semi-discrete limit of our main result.