The combinatorial R-matrix is the unique affine sl_n crystal isomorphism between A x B and B x A, where A and B are finite-dimensional affine crystals corresponding to rectangular partitions. This map can be described combinatorially in terms of rectification of skew tableaux.

In this talk, I will present a construction of a ``geometric R-matrix,'' a rational map which has properties analogous to those of the combinatorial R-matrix, and which tropicalizes to a piecewise-linear formula for the combinatorial R-matrix. The construction makes use of Noumi and Yamada's notion of ``tropical row insertion,'' as well as the Grassmannian and the loop group. When both partitions are a single row, we recover results of Yamada and Lam-Pylyavskyy. Speaker(s): Gabriel Frieden (U. Michigan)