Kirillov-Reshetikhin modules and quantum $K$-matrices

TL;DR

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Contribution

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Abstract

From a quantum $K$-matrix of the fundamental representation, we construct one for the Kirillov-Reshetikhin module by fusion construction. Using the $\imath$crystal theory by the last author, we also obtain combinatorial $K$-matrices corresponding to the symmetric tensor representations of affine type $A$ for all quasi-split Satake diagrams.