Date: Friday, January 27, 2017
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: A rational lift of the combinatorial Rmatrix
Abstract: The combinatorial Rmatrix is the unique affine sl_n crystal isomorphism between A x B and B x A, where A and B are finitedimensional 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 Rmatrix,'' a rational map which has properties analogous to those of the combinatorial Rmatrix, and which tropicalizes to a piecewiselinear formula for the combinatorial Rmatrix. 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 LamPylyavskyy.
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Speaker: Gabriel Frieden
Institution: U. Michigan
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