Kirillov–Reshetikhin Modules and Quantum K-matrices

From a quantum K-matrix of a fundamental representation of any quantum affine algebra, we construct one for the Kirillov–Reshetikhin module by fusion construction. Using the \(\imath \) $ı$ 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.