English

The Robinson-Schensted-Knuth correspondence describes a bijection between matrices with non-negative integers entries and pairs of semistandard Young Tableaux of the same shape. The algorithm describing this correspondence is by no means obvious. The question which motivated this work was whether the RSK-Algorithm is canonical from the point of view of representation theory. We realize the RSK correspondence as a correspondence between two parametrizations of the crystal basis of the algebra of quantum matrices, which is a representation of a quantum group. The main technical point is to prove the compatibility of Kashiwara operators with the RSK correspondence.

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