Seminar Event Detail


Combinatorics

Date:  Friday, January 27, 2017
Location:  4088 East Hall (3:10 PM to 4:00 PM)

Title:  A rational lift of the combinatorial R-matrix

Abstract:   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.

Files:


Speaker:  Gabriel Frieden
Institution:  U. Michigan

Event Organizer:     

 

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