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Séminaire Lotharingien de Combinatoire, 78B.46 (2017), 12 pp.

# Gabriel Frieden

# Rational Lift of the Combinatorial *R*-Matrix

**Abstract.**
We present a rational lift of the combinatorial *R*-matrix for tensor
products of rectangular tableaux. The key ingredients are a connection
between the product of rectangular tableaux (in the plactic monoid)
and multiplication of certain "tableau matrices," and a birational
map from these matrices to the Grassmannian.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

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